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Published: 4 June 2021
Last updated: 29 January 2023

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1

Hutzenthaler, Martin, and Jesse Earl Taylor. "Time reversal of some stationary jump diffusion processes from population genetics." Advances in Applied Probability 42, no. 4 (December 2010): 1147–71. http://dx.doi.org/10.1239/aap/1293113155.

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We describe the processes obtained by time reversal of a class of stationary jump diffusion processes that model the dynamics of genetic variation in populations subject to repeated bottlenecks. Assuming that only one lineage survives each bottleneck, the forward process is a diffusion on [0,1] that jumps to the boundary before diffusing back into the interior. We show that the behavior of the time-reversed process depends on whether the boundaries are accessible to the diffusive motion of the forward process. If a boundary point is inaccessible to the forward diffusion then time reversal leads to a jump diffusion that jumps immediately into the interior whenever it arrives at that point. If, instead, a boundary point is accessible then the jumps off of that point are governed by a weighted local time of the time-reversed process.
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2

Hutzenthaler, Martin, and Jesse Earl Taylor. "Time reversal of some stationary jump diffusion processes from population genetics." Advances in Applied Probability 42, no. 04 (December 2010): 1147–71. http://dx.doi.org/10.1017/s0001867800004560.

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We describe the processes obtained by time reversal of a class of stationary jump diffusion processes that model the dynamics of genetic variation in populations subject to repeated bottlenecks. Assuming that only one lineage survives each bottleneck, the forward process is a diffusion on [0,1] that jumps to the boundary before diffusing back into the interior. We show that the behavior of the time-reversed process depends on whether the boundaries are accessible to the diffusive motion of the forward process. If a boundary point is inaccessible to the forward diffusion then time reversal leads to a jump diffusion that jumps immediately into the interior whenever it arrives at that point. If, instead, a boundary point is accessible then the jumps off of that point are governed by a weighted local time of the time-reversed process.
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3

Davis, Mark, and Sébastien Lleo. "Jump-Diffusion Risk-Sensitive Asset Management II: Jump-Diffusion Factor Model." SIAM Journal on Control and Optimization 51, no. 2 (January 2013): 1441–80. http://dx.doi.org/10.1137/110825881.

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4

Liu, Weijie, Yan Shen, and Lijuan Shen. "Degradation Modeling for Lithium-Ion Batteries with an Exponential Jump-Diffusion Model." Mathematics 10, no. 16 (August 19, 2022): 2991. http://dx.doi.org/10.3390/math10162991.

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The degradation of Lithium-ion batteries is usually measured by capacity loss. When batteries deteriorate with usage, the capacities would generally have a declining trend. However, occasionally, considerable capacity regeneration may occur during the degradation process. To better capture the coexistence of capacity loss and regeneration, this paper considers a jump-diffusion model with jumps subject to the exponential distribution. For estimation of model parameters, a jump detection test is first adopted to identify jump arrival times and separate observation data into two series, jump series and diffusion series; then, with the help of probabilistic programming, the Markov chain Monte Carlo sampling algorithm is used to estimate the parameters for the jump and diffusion parts of the degradation model, respectively. The distribution functions of failure time and residual useful life are also approximated by the Monte Carlo simulation approach. Simulation results show the feasibility and good performance of the combined estimation method. Finally, real data analysis indicates that the jump-diffusion process model with the combined estimation method could give a more accurate estimation when predicting the failure time of the battery.
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5

Wang, Zhouwei, Qicheng Zhao, Min Zhu, and Tao Pang. "Jump Aggregation, Volatility Prediction, and Nonlinear Estimation of Banks’ Sustainability Risk." Sustainability 12, no. 21 (October 25, 2020): 8849. http://dx.doi.org/10.3390/su12218849.

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Extreme financial events usually lead to sharp jumps in stock prices and volatilities. In addition, jump clustering and stock price correlations contribute to the risk amplification acceleration mechanism during the crisis. In this paper, four Jump-GARCH models are used to forecast the jump diffusion volatility, which is used as the risk factor. The linear and asymmetric nonlinear effects are considered, and the value at risk of banks is estimated by support vector quantile regression. There are three main findings. First, in terms of the volatility process of bank stock price, the Jump Diffusion GARCH model is better than the Continuous Diffusion GARCH model, and the discrete jump volatility is significant. Secondly, due to the difference of the sensitivity of abnormal information shock, the jump behavior of bank stock price is heterogeneous. Moreover, CJ-GARCH models are suitable for most banks, while ARJI-R2-GARCH models are more suitable for small and medium sized banks. Thirdly, based on the jump diffusion volatility information, the performance of the support vector quantile regression is better than that of the parametric quantile regression and nonparametric quantile regression.
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6

Zheng, Yingchun, and Yunfeng Yang. "Wealth optimization models on jump-diffusion model." Journal of Interdisciplinary Mathematics 21, no. 1 (January 2, 2018): 201–12. http://dx.doi.org/10.1080/09720502.2017.1406629.

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7

Deng, Guohe. "Option Pricing under Two-Factor Stochastic Volatility Jump-Diffusion Model." Complexity 2020 (September 1, 2020): 1–15. http://dx.doi.org/10.1155/2020/1960121.

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Empirical evidence shows that single-factor stochastic volatility models are not flexible enough to account for the stochastic behavior of the skew, and certain financial assets may exhibit jumps in returns and volatility. This paper introduces a two-factor stochastic volatility jump-diffusion model in which two variance processes with jumps drive the underlying stock price and then considers the valuation on European style option. We derive a semianalytical formula for European vanilla option and develop a fast and accurate numerical algorithm for the computation of the option prices using the fast Fourier transform (FFT) technique. We compare the volatility smile and probability density of the proposed model with those of alternative models, including the normal jump diffusion model and single-factor stochastic volatility model with jumps, respectively. Finally, we provide some sensitivity analysis of the model parameters to the options and several calibration tests using option market data. Numerical examples show that the proposed model has more flexibility to capture the implied volatility term structure and is suitable for empirical work in practice.
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8

Jiahui, Yang, Zhou Shengwu, Zhou Haitao, and Guo Kaiqiang. "Pricing Vulnerable Option under Jump-Diffusion Model with Incomplete Information." Discrete Dynamics in Nature and Society 2019 (May 20, 2019): 1–8. http://dx.doi.org/10.1155/2019/5848375.

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In this paper, the closed-form pricing formula for the European vulnerable option with credit risk and jump risk under incomplete information was derived. Noise was introduced to the option writers assets while the underlying asset price and the value of corporation were assumed to follow the jump-diffusion processes. Finally the numerical experiment showed that jumps of underlying assets would increase the value of the option, but noise of corporation value was opposite.
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9

Li, Dan, Jing’an Cui, and Guohua Song. "Asymptotic Behaviour and Extinction of Delay Lotka-Volterra Model with Jump-Diffusion." Journal of Applied Mathematics 2014 (2014): 1–16. http://dx.doi.org/10.1155/2014/249504.

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This paper studies the effect of jump-diffusion random environmental perturbations on the asymptotic behaviour and extinction of Lotka-Volterra population dynamics with delays. The contributions of this paper lie in the following: (a) to consider delay stochastic differential equation with jumps, we introduce a proper initial data space, in which the initial data may be discontinuous function with downward jumps; (b) we show that the delay stochastic differential equation with jumps associated with our model has a unique global positive solution and give sufficient conditions that ensure stochastically ultimate boundedness, moment average boundedness in time, and asymptotic polynomial growth of our model; (c) the sufficient conditions for the extinction of the system are obtained, which generalized the former results and showed that the sufficiently large random jump magnitudes and intensity (average rate of jump events arrival) may lead to extinction of the population.
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10

Li, Hua, Yu-Hang Chen, and Bin-Ze Tang. "A revised jump-diffusion and rotation-diffusion model." Chinese Physics B 28, no. 5 (May 2019): 056105. http://dx.doi.org/10.1088/1674-1056/28/5/056105.

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11

Liu, Shican, Yanli Zhou, Yonghong Wu, and Xiangyu Ge. "Option Pricing under the Jump Diffusion and Multifactor Stochastic Processes." Journal of Function Spaces 2019 (February 3, 2019): 1–12. http://dx.doi.org/10.1155/2019/9754679.

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In financial markets, there exists long-observed feature of the implied volatility surface such as volatility smile and skew. Stochastic volatility models are commonly used to model this financial phenomenon more accurately compared with the conventional Black-Scholes pricing models. However, one factor stochastic volatility model is not good enough to capture the term structure phenomenon of volatility smirk. In our paper, we extend the Heston model to be a hybrid option pricing model driven by multiscale stochastic volatility and jump diffusion process. In our model the correlation effects have been taken into consideration. For the reason that the combination of multiscale volatility processes and jump diffusion process results in a high dimensional differential equation (PIDE), an efficient finite element method is proposed and the integral term arising from the jump term is absorbed to simplify the problem. The numerical results show an efficient explanation for volatility smirks when we incorporate jumps into both the stock process and the volatility process.
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12

Vittal, P. R., M. Venkateswaran, and P. R. S. Reddy. "Stochastic Storage Model with Jump-Diffusion." Journal of the Indian Society for Probability and Statistics 18, no. 1 (December 1, 2016): 53–76. http://dx.doi.org/10.1007/s41096-016-0013-5.

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13

Chen, Kuo-Shing, and Yu-Chuan Huang. "Detecting Jump Risk and Jump-Diffusion Model for Bitcoin Options Pricing and Hedging." Mathematics 9, no. 20 (October 13, 2021): 2567. http://dx.doi.org/10.3390/math9202567.

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In this paper, we conduct a fast calibration in the jump-diffusion model to capture the Bitcoin price dynamics, as well as the behavior of some components affecting the price itself, such as the risk of pitfalls and its ambiguous effect on the evolution of Bitcoin’s price. In addition, in our study of the Bitcoin option pricing, we find that the inclusion of jumps in returns and volatilities are significant in the historical time series of Bitcoin prices. The benefits of incorporating these jumps flow over into option pricing, as well as adequately capture the volatility smile in option prices. To the best of our knowledge, this is the first work to analyze the phenomenon of price jump risk and to interpret Bitcoin option valuation as “exceptionally ambiguous”. Crucially, using hedging options for the Bitcoin market, we also prove some important properties: Bitcoin options follow a convex, but not strictly convex function. This property provides adequate risk assessment for convex risk measure.
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14

Kostrzewski, Maciej, and Jadwiga Kostrzewska. "The Impact of Forecasting Jumps on Forecasting Electricity Prices." Energies 14, no. 2 (January 9, 2021): 336. http://dx.doi.org/10.3390/en14020336.

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The paper is devoted to forecasting hourly day-ahead electricity prices from the perspective of the existence of jumps. We compare the results of different jump detection techniques and identify common features of electricity price jumps. We apply the jump-diffusion model with a double exponential distribution of jump sizes and explanatory variables. In order to improve the accuracy of electricity price forecasts, we take into account the time-varying intensity of price jump occurrences. We forecast moments of jump occurrences depending on several factors, including seasonality and weather conditions, by means of the generalised ordered logit model. The study is conducted on the basis of data from the Nord Pool power market. The empirical results indicate that the model with the time-varying intensity of jumps and a mechanism of jump prediction is useful in forecasting electricity prices for peak hours, i.e., including the probabilities of downward, no or upward jump occurrences into the model improves the forecasts of electricity prices.
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15

Kostrzewski, Maciej, and Jadwiga Kostrzewska. "The Impact of Forecasting Jumps on Forecasting Electricity Prices." Energies 14, no. 2 (January 9, 2021): 336. http://dx.doi.org/10.3390/en14020336.

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The paper is devoted to forecasting hourly day-ahead electricity prices from the perspective of the existence of jumps. We compare the results of different jump detection techniques and identify common features of electricity price jumps. We apply the jump-diffusion model with a double exponential distribution of jump sizes and explanatory variables. In order to improve the accuracy of electricity price forecasts, we take into account the time-varying intensity of price jump occurrences. We forecast moments of jump occurrences depending on several factors, including seasonality and weather conditions, by means of the generalised ordered logit model. The study is conducted on the basis of data from the Nord Pool power market. The empirical results indicate that the model with the time-varying intensity of jumps and a mechanism of jump prediction is useful in forecasting electricity prices for peak hours, i.e., including the probabilities of downward, no or upward jump occurrences into the model improves the forecasts of electricity prices.
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16

Gómez-Valle, Lourdes, and Julia Martínez-Rodríguez. "Including Jumps in the Stochastic Valuation of Freight Derivatives." Mathematics 9, no. 2 (January 13, 2021): 154. http://dx.doi.org/10.3390/math9020154.

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The spot freight rate processes considered in the literature for pricing forward freight agreements (FFA) and freight options usually have a particular dynamics in order to obtain the prices. In those cases, the FFA prices are explicitly obtained. However, for jump-diffusion models, an exact solution is not known for the freight options (Asian-type), in part due to the absence of a suitable valuation framework. In this paper, we consider a general jump-diffusion process to describe the spot freight dynamics and we obtain exact solutions of FFA prices for two parametric models. Moreover, we develop a partial integro-differential equation (PIDE), for pricing freight options for a general unifactorial jump-diffusion model. When we consider that the spot freight follows a geometric process with jumps, we obtain a solution of the freight option price in a part of its domain. Finally, we show the effect of the jumps in the FFA prices by means of numerical simulations.
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17

MERINO, R., J. POSPÍŠIL, T. SOBOTKA, and J. VIVES. "DECOMPOSITION FORMULA FOR JUMP DIFFUSION MODELS." International Journal of Theoretical and Applied Finance 21, no. 08 (December 2018): 1850052. http://dx.doi.org/10.1142/s0219024918500528.

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In this paper, we derive a generic decomposition of the option pricing formula for models with finite activity jumps in the underlying asset price process (SVJ models). This is an extension of the well-known result by Alòs [(2012) A decomposition formula for option prices in the Heston model and applications to option pricing approximation, Finance and Stochastics 16 (3), 403–422, doi: https://doi.org/10.1007/s00780-012-0177-0 ] for Heston [(1993) A closed-form solution for options with stochastic volatility with applications to bond and currency options, The Review of Financial Studies 6 (2), 327–343, doi: https://doi.org/10.1093/rfs/6.2.327 ] SV model. Moreover, explicit approximation formulas for option prices are introduced for a popular class of SVJ models — models utilizing a variance process postulated by Heston [(1993) A closed-form solution for options with stochastic volatility with applications to bond and currency options, The Review of Financial Studies 6 (2), 327–343, doi: https://doi.org/10.1093/rfs/6.2.327 ]. In particular, we inspect in detail the approximation formula for the Bates [(1996), Jumps and stochastic volatility: Exchange rate processes implicit in Deutsche mark options, The Review of Financial Studies 9 (1), 69–107, doi: https://doi.org/10.1093/rfs/9.1.69 ] model with log-normal jump sizes and we provide a numerical comparison with the industry standard — Fourier transform pricing methodology. For this model, we also reformulate the approximation formula in terms of implied volatilities. The main advantages of the introduced pricing approximations are twofold. Firstly, we are able to significantly improve computation efficiency (while preserving reasonable approximation errors) and secondly, the formula can provide an intuition on the volatility smile behavior under a specific SVJ model.
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18

Masoliver, Jaume, Miquel Montero, and Josep Perelló. "Jump-Diffusion Models for Valuing the Future: Discounting under Extreme Situations." Mathematics 9, no. 14 (July 6, 2021): 1589. http://dx.doi.org/10.3390/math9141589.

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We develop the process of discounting when underlying rates follow a jump-diffusion process, that is, when, in addition to diffusive behavior, rates suffer a series of finite discontinuities located at random Poissonian times. Jump amplitudes are also random and governed by an arbitrary density. Such a model may describe the economic evolution, specially when extreme situations occur (pandemics, global wars, etc.). When, between jumps, the dynamical evolution is governed by an Ornstein–Uhlenbeck diffusion process, we obtain exact and explicit expressions for the discount function and the long-run discount rate and show that the presence of discontinuities may drastically reduce the discount rate, a fact that has significant consequences for environmental planning. We also discuss as a specific example the case when rates are described by the continuous time random walk.
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19

LI, T. RAY, and MARIANITO R. RODRIGO. "Alternative results for option pricing and implied volatility in jump-diffusion models using Mellin transforms." European Journal of Applied Mathematics 28, no. 5 (December 6, 2016): 789–826. http://dx.doi.org/10.1017/s0956792516000516.

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In this article, we use Mellin transforms to derive alternative results for option pricing and implied volatility estimation when the underlying asset price is governed by jump-diffusion dynamics. The current well known results are restrictive since the jump is assumed to follow a predetermined distribution (e.g., lognormal or double exponential). However, the results we present are general since we do not specify a particular jump-diffusion model within the derivations. In particular, we construct and derive an exact solution to the option pricing problem in a general jump-diffusion framework via Mellin transforms. This approach of Mellin transforms is further extended to derive a Dupire-like partial integro-differential equation, which ultimately yields an implied volatility estimator for assets subjected to instantaneous jumps in the price. Numerical simulations are provided to show the accuracy of the estimator.
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20

Zhang, Su-mei, and Li-he Wang. "A Fast Fourier Transform Technique for Pricing European Options with Stochastic Volatility and Jump Risk." Mathematical Problems in Engineering 2012 (2012): 1–17. http://dx.doi.org/10.1155/2012/761637.

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We consider European options pricing with double jumps and stochastic volatility. We derived closed-form solutions for European call options in a double exponential jump-diffusion model with stochastic volatility (SVDEJD). We developed fast and accurate numerical solutions by using fast Fourier transform (FFT) technique. We compared the density of our model with those of other models, including the Black-Scholes model and the double exponential jump-diffusion model. At last, we analyzed several effects on option prices under the proposed model. Simulations show that the SVDEJD model is suitable for modelling the long-time real-market changes and stock returns are negatively correlated with volatility. The model and the proposed option pricing method are useful for empirical analysis of asset returns and managing the corporate credit risks.
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21

Lee, Kiseop, and Seongjoo Song. "Insiders' hedging in a jump diffusion model." Quantitative Finance 7, no. 5 (October 2007): 537–45. http://dx.doi.org/10.1080/14697680601043191.

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22

Kou, S. G. "A Jump-Diffusion Model for Option Pricing." Management Science 48, no. 8 (August 2002): 1086–101. http://dx.doi.org/10.1287/mnsc.48.8.1086.166.

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23

Gelin, M. F., and D. S. Kosov. "Microscopic origin of the jump diffusion model." Journal of Chemical Physics 130, no. 13 (April 7, 2009): 134502. http://dx.doi.org/10.1063/1.3103263.

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24

Fadonougbo, Renaud, and George O. Orwa. "Jump Adapted Scheme Of a Non Mark Dependent Jump Diffusion Process with Application to the Merton Jump Diffusion Model." International Journal of Statistics and Probability 5, no. 4 (June 26, 2017): 80. http://dx.doi.org/10.5539/ijsp.v6n4p80.

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This paper provides a complete proof of the strong convergence of the Jump adapted discretization Scheme in the univariate and mark independent jump diffusion process case. We put in detail and clearly a known and general result for mark dependent jump diffusion process. A Monte-Carlo simulation is used as well to show numerical evidence.
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25

Siu, Tak Kuen, John W. Lau, and Hailiang Yang. "Pricing Participating Products under a Generalized Jump-Diffusion Model." Journal of Applied Mathematics and Stochastic Analysis 2008 (July 13, 2008): 1–30. http://dx.doi.org/10.1155/2008/474623.

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We propose a model for valuing participating life insurance products under a generalized jump-diffusion model with a Markov-switching compensator. It also nests a number of important and popular models in finance, including the classes of jump-diffusion models and Markovian regime-switching models. The Esscher transform is employed to determine an equivalent martingale measure. Simulation experiments are conducted to illustrate the practical implementation of the model and to highlight some features that can be obtained from our model.
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26

Li, Zhe. "Equity Option Pricing with Systematic and Idiosyncratic Volatility and Jump Risks." Journal of Risk and Financial Management 13, no. 1 (January 17, 2020): 16. http://dx.doi.org/10.3390/jrfm13010016.

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Recently, a large number of empirical studies indicated that individual equity options exhibit a strong factor structure. In this paper, the importance of systematic and idiosyncratic volatility and jump risks on individual equity option pricing is analyzed. First, we propose a new factor structure model for pricing the individual equity options with stochastic volatility and jumps, which takes into account four types of risks, i.e., the systematic diffusion, the idiosyncratic diffusion, the systematic jump, and the idiosyncratic jump. Second, we derive the closed-form solutions for the prices of both the market index and individual equity options by utilizing the Fourier inversion. Finally, empirical studies are carried out to show the superiority of our model based on the S&P 500 index and the stock of Apple Inc. on options. The out-of-sample pricing performance of our proposed model outperforms the other three benchmark models especially for short term and deep out-of-the-money options.
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27

Davis, Mark, and Sébastien Lleo. "Jump-Diffusion Risk-Sensitive Asset Management I: Diffusion Factor Model." SIAM Journal on Financial Mathematics 2, no. 1 (January 2011): 22–54. http://dx.doi.org/10.1137/090760180.

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28

Tan, Xiaoyu, Shenghong Li, and Shuyi Wang. "Pricing European-Style Options in General Lévy Process with Stochastic Interest Rate." Mathematics 8, no. 5 (May 6, 2020): 731. http://dx.doi.org/10.3390/math8050731.

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This paper extends the traditional jump-diffusion model to a comprehensive general Lévy process model with the stochastic interest rate for European-style options pricing. By using the Girsanov theorem and Itô formula, we derive the uniform formalized pricing formulas under the equivalent martingale measure. This model contains not only the traditional jump-diffusion model, such as the compound Poisson model, the renewal model, the pure-birth jump-diffusion model, but also the infinite activities Lévy model.
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29

Tong, Jinying. "Feller Property for a Special Hybrid Jump-Diffusion Model." Abstract and Applied Analysis 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/412848.

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We consider the stochastic stability for a hybrid jump-diffusion model, where the switching here is a phase semi-Markovian process. We first transform the process into a corresponding jump-diffusion with Markovian switching by the supplementary variable technique. Then we prove the Feller and strong Feller properties of the model under some assumptions.
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30

Peng, Bo, and Zhi Hui Wu. "Pricing Option on Jump Diffusion and Stochastic Interest Rates Model." Applied Mechanics and Materials 50-51 (February 2011): 723–27. http://dx.doi.org/10.4028/www.scientific.net/amm.50-51.723.

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This paper assumed that the stock price jump process for a special kind of renewal jump process, that is incident time interval for independent and subordinate to Gamma distribution random variable sequence. We obtain the European bi-direction option pricing formulas on jump diffusion model under the stochastic interest rates by simply mathematical induce by means of martingale method.
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31

BROADIE, MARK, and ASHISH JAIN. "THE EFFECT OF JUMPS AND DISCRETE SAMPLING ON VOLATILITY AND VARIANCE SWAPS." International Journal of Theoretical and Applied Finance 11, no. 08 (December 2008): 761–97. http://dx.doi.org/10.1142/s0219024908005032.

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We investigate the effect of discrete sampling and asset price jumps on fair variance and volatility swap strikes. Fair discrete volatility strikes and fair discrete variance strikes are derived in different models of the underlying evolution of the asset price: the Black-Scholes model, the Heston stochastic volatility model, the Merton jump-diffusion model and the Bates and Scott stochastic volatility and jump model. We determine fair discrete and continuous variance strikes analytically and fair discrete and continuous volatility strikes using simulation and variance reduction techniques and numerical integration techniques in all models. Numerical results show that the well-known convexity correction formula may not provide a good approximation of fair volatility strikes in models with jumps in the underlying asset. For realistic contract specifications and model parameters, we find that the effect of discrete sampling is typically small while the effect of jumps can be significant.
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32

Weron, Karina, Aleksander Stanislavsky, Agnieszka Jurlewicz, Mark M. Meerschaert, and Hans-Peter Scheffler. "Clustered continuous-time random walks: diffusion and relaxation consequences." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2142 (February 2012): 1615–28. http://dx.doi.org/10.1098/rspa.2011.0697.

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We present a class of continuous-time random walks (CTRWs), in which random jumps are separated by random waiting times. The novel feature of these CTRWs is that the jumps are clustered. This introduces a coupled effect, with longer waiting times separating larger jump clusters. We show that the CTRW scaling limits are time-changed processes. Their densities solve two different fractional diffusion equations, depending on whether the waiting time is coupled to the preceding jump, or the following one. These fractional diffusion equations can be used to model all types of experimentally observed two power-law relaxation patterns. The parameters of the scaling limit process determine the power-law exponents and loss peak frequencies.
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33

LO, HARRY, and ALEKSANDAR MIJATOVIĆ. "VOLATILITY DERIVATIVES IN MARKET MODELS WITH JUMPS." International Journal of Theoretical and Applied Finance 14, no. 07 (November 2011): 1159–93. http://dx.doi.org/10.1142/s0219024911006656.

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It is well documented that a model for the underlying asset price process that seeks to capture the behaviour of the market prices of vanilla options needs to exhibit both diffusion and jump features. In this paper we assume that the asset price process S is Markov with càdlàg paths and propose a scheme for computing the law of the realized variance of the log returns accrued while the asset was trading in a prespecified corridor. We thus obtain an algorithm for pricing and hedging volatility derivatives and derivatives on the corridor-realized variance in such a market. The class of models under consideration is large, as it encompasses jump-diffusion and Lévy processes. We prove the weak convergence of the scheme and describe in detail the implementation of the algorithm in the characteristic cases where S is a CEV process (continuous trajectories), a variance gamma process (jumps with independent increments) or an infinite activity jump-diffusion (discontinuous trajectories with dependent increments).
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34

EDDAHBI, M'HAMED, SIDI MOHAMED LALAOUI BEN CHERIF, and ABDELAZIZ NASROALLAH. "COMPUTATION OF GREEKS FOR JUMP-DIFFUSION MODELS." International Journal of Theoretical and Applied Finance 18, no. 06 (September 2015): 1550039. http://dx.doi.org/10.1142/s0219024915500399.

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In the present paper, we compute the Greeks for a class of jump diffusion models by using Malliavin calculus techniques. More precisely, the model under consideration is governed by a Brownian component and a jump part described by a compound Poisson process. Our approach consists of approximating the compound Poisson process by a suitable sequence of standard Poisson processes. The Greeks of the original model are obtained as limits or weighted limits of the Greeks of the approximate model. We illustrate our results by the computation of the Greeks for digital options in the framework of the Merton model. The technique of Malliavin weights is found to be efficient compared to the finite difference approach.
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35

CHIARELLA, CARL, CHRISTINA NIKITOPOULOS SKLIBOSIOS, and ERIK SCHLÖGL. "A MARKOVIAN DEFAULTABLE TERM STRUCTURE MODEL WITH STATE DEPENDENT VOLATILITIES." International Journal of Theoretical and Applied Finance 10, no. 01 (February 2007): 155–202. http://dx.doi.org/10.1142/s0219024907004147.

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The defaultable forward rate is modelled as a jump diffusion process within the Schönbucher [26,27] general Heath, Jarrow and Morton [20] framework where jumps in the defaultable term structure fd(t,T) cause jumps and defaults to the defaultable bond prices Pd(t,T). Within this framework, we investigate an appropriate forward rate volatility structure that results in Markovian defaultable spot rate dynamics. In particular, we consider state dependent Wiener volatility functions and time dependent Poisson volatility functions. The corresponding term structures of interest rates are expressed as finite dimensional affine realizations in terms of benchmark defaultable forward rates. In addition, we extend this model to incorporate stochastic spreads by allowing jump intensities to follow a square-root diffusion process. In that case the dynamics become non-Markovian and to restore path independence we propose either an approximate Markovian scheme or, alternatively, constant Poisson volatility functions. We also conduct some numerical simulations to gauge the effect of the stochastic intensity and the distributional implications of various volatility specifications.
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36

KUNITA, HIROSHI, and TAKUYA YAMADA. "AVERAGE OPTIONS FOR JUMP DIFFUSION MODELS." Asia-Pacific Journal of Operational Research 27, no. 02 (April 2010): 143–66. http://dx.doi.org/10.1142/s0217595910002612.

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In this paper, we study the problem of pricing average strike options in the case where the price processes are jump diffusion processes. As to the striking value we take the geometric average of the price process. Two cases are studied in details: One is the case where the jumping law of the price process is subject to a Gaussian distribution called Merton model, and the other is the case where the jumping law is subject to a double exponential distribution called Kou model. In both cases the price of the average strike option is represented as a time average of a suitable European put option.
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37

Li, Xiaoping, and Chunyang Zhou. "Dynamic asset allocation with asymmetric jump distribution." China Finance Review International 8, no. 4 (November 19, 2018): 387–98. http://dx.doi.org/10.1108/cfri-08-2017-0180.

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Purpose The purpose of this paper is to solve the optimal dynamic portfolio problem under the double-exponential jump diffusion (DEJD) distribution, which can allow the asset returns to jump asymmetrically. Design/methodology/approach The authors solve the problem by solving the HJB equation. Meanwhile, in the presence of jump component in the asset returns, the investor may suffer a large loss due to high leveraged position, so the authors impose the short-sale and borrowing constraints when solving the optimization problem. Findings The authors provide sufficient conditions such that the optimal solution exists and show theoretically that the optimal risky asset weight is an increasing function of jump-up probability and average jump-up size and a decreasing function of average jump-down size. Research limitations/implications In this study, the authors assume that the jump-up and jump-down intensities are constant. In the future, the authors will relax the assumption and allows the jump intensities to be time varying. Practical implications Empirical studies based on Chinese Shanghai stock index data show that the jump distribution of Shanghai index returns is asymmetric, and the DEJD model can fit the data better than the log-normal jump-diffusion model. The numerical results are consistent with the theoretical prediction, and the authors find that the less risk-averse investor will suffer more economic cost if ignoring asymmetric jump distribution. Originality/value This study first examines how asymmetric jumps affect the investor’s portfolio allocation.
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38

Singh, Vipul Kumar. "Pricing competitiveness of jump-diffusion option pricing models: evidence from recent financial upheavals." Studies in Economics and Finance 32, no. 3 (August 3, 2015): 357–78. http://dx.doi.org/10.1108/sef-08-2012-0099.

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Purpose – The purpose of this paper is to investigate empirically the forecasting performance of jump-diffusion option pricing models of (Merton and Bates) with the benchmark Black–Scholes (BS) model relative to market, for pricing Nifty index options of India. The specific period chosen for this study canvasses the extreme up and down limits (jumps) of the Indian capital market. In addition, equity markets keep on facing high and low tides of financial flux amid new economic and financial considerations. With this backdrop, the paper focuses on finding an impeccable option-pricing model which can meet the requirements of option traders and practitioners during tumultuous periods in the future. Design/methodology/approach – Envisioning the fact, the all option-pricing models normally does wrong valuation relative to market. For estimating the structural parameters that governs the underlying asset distribution purely from the underlying asset return data, we have used the nonlinear least-square method. As an approach, we analyzed model prices by dividing the option data into 15 moneyness-maturity groups – depending on the time to maturity and strike price. The prices are compared analytically by continuously updating the parameters of two models using cross-sectional option data on daily basis. Estimated parameters then used to figure out the forecasting performance of models with corresponding BS and market – for pricing day-ahead option prices and implied volatility. Findings – The outcomes of the paper reveal that the jump-diffusion models are a better substitute of classical BS, thus improving the pricing bias significantly. But compared to jump-diffusion model of Merton’s, the model of Bates’ can be applied more uniquely to find out the pricing of three popularly traded categories: deep-out-of-the-money, out-of-the-money and at-the-money of Nifty index options. Practical implications – The outcome of this research work reveals that the jumps are important components of pricing dynamics of Nifty index options. Incorporation of jump-diffusion process into option pricing of Nifty index options leads to a higher pricing effectiveness, reduces the pricing bias and gives values closer to the market. As the models have been tested in extreme conditions to determine the dominant effectuality, the outcome of this paper helps traders in keeping the investment protected under normal conditions. Originality/value – The specific period chosen for this study is very unique; it canvasses the extreme up and down limits (jumps) of the Indian capital market and provides the most apt situation for testifying the pricing competitiveness of the models in question. To testify the robustness of models, they have been put into a practical implication of complete cycle of financial frame.
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39

Chung, Tsz Kin, and Yue Kuen Kwok. "Equity-credit modeling under affine jump-diffusion models with jump-to-default." Journal of Financial Engineering 01, no. 02 (June 2014): 1450017. http://dx.doi.org/10.1142/s2345768614500172.

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This paper considers the stochastic models for pricing credit-sensitive financial derivatives using the joint equity-credit modeling approach. The modeling of credit risk is embedded into a stochastic asset dynamics model by adding the jump-to-default (JtD) feature. We discuss the class of stochastic affine jump-diffusion (AJD) models with JtD and apply the models to price defaultable European options and credit default swaps. Numerical studies of the equity-credit models are also considered. The impact on the pricing behavior of derivative products with the added JtD feature is examined.
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40

Gosain, K. L., D. K. Chaturvedi, Irina V. Belova, and Graeme E. Murch. "Tracer Diffusion by Six-Jump-Cycles in Nonstoichiometric B2 Intermetallic Compounds." Defect and Diffusion Forum 247-248 (December 2005): 9–20. http://dx.doi.org/10.4028/www.scientific.net/ddf.247-248.9.

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Tracer diffusion in non-stoichiometric B2 intermetallic compounds having antistructural disorder is investigated using the six-jump-cycle (6JC) as a fundamental diffusion unit. For non-stoichiometric compositions, the antistructural atoms are assumed to be isolated and located at one of the six [110]-type and [100]-type sites (as only these sites are involved in the 6JC or 2JC). The jump frequencies for the 6JC involving a perfectly ordered configuration are calculated in terms of a four-frequency-model, using the meanfirst- passage concept of Arita et al. The jump frequency of an antistructural atom at [110] or [100]-type sites is taken to be the harmonic mean of frequencies of two successive nearestneighbour jumps of the same kind of atoms. The expressions for the tracer diffusion coefficients are derived for both atomic components at deviations from stoichiometry, assuming that the 6JC mechanism is valid. The results are compared with Monte Carlo simulations based on single vacancy jumps and found to be in fair agreement for compositions close to stoichiometry.
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41

Collins, Gary S. "Diffusion and Equilibration of Site-Preferences Following Transmutation of Tracer Atoms." Diffusion Foundations 19 (November 2018): 61–79. http://dx.doi.org/10.4028/www.scientific.net/df.19.61.

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Using the method of perturbed angular correlation of gamma rays, diffusional jump-frequencies of probe atoms can be measured through relaxation of the nuclear quadrupole interaction. This was first shown in 2004 for jumps of tracer atoms that lead to reorientation of the local electric field-gradient, such as jumps on the connected a-sublattice in the L12 crystal structure. Studies on many such phases using the 111In/Cd PAC probe are reviewed in this paper. A major finding from a 2009 study of indides of rare-earth elements, In3R, was the apparent observation of two diffusional regimes: one dominant for heavy-lanthanide phases, R= Lu, Tm, Er, Dy, Tb, Gd, that was consistent with a simple model of vacancy diffusion on the In a-sublattice, and another for light-lanthanides, R= La, Ce, Pr, Nd, that had no obvious explanation but for which several alternative diffusion mechanisms were suggested. It is herein proposed that the latter regime arises not from a diffusion mechanism but from transfer of Cd-probes from In-sites where they originate to R-sites as a consequence of a change in site-preference of 111Cd-daughter atoms from In-sites to R-sites following transmutation of 111In. Support for this transfer mechanism comes from a study of site-preferences and jump-frequencies of 111In/Cd probes in Pd3R phases. Possible mechanisms for transfer are described, with the most likely mechanism identified as one in which Cd-probes on a-sites transfer to interstitial sites, diffuse interstitially, and then react with vacancies on b-sites. Implications of this proposal are discussed. For indides of heavy-lanthanide elements, the Cd-tracer remains on the In-sublattice and relaxation gives the diffusional jump-frequency.
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42

Liu, Shican, Yu Yang, Hu Zhang, and Yonghong Wu. "Variance Swap Pricing under Markov-Modulated Jump-Diffusion Model." Discrete Dynamics in Nature and Society 2021 (January 8, 2021): 1–16. http://dx.doi.org/10.1155/2021/9814605.

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This paper investigates the pricing of discretely sampled variance swaps under a Markov regime-switching jump-diffusion model. The jump diffusion, as well as other parameters of the underlying stock’s dynamics, is modulated by a Markov chain representing different states of the market. A semi-closed-form pricing formula is derived by applying the generalized Fourier transform method. The counterpart pricing formula for a variance swap with continuous sampling times is also derived and compared with the discrete price to show the improvement of accuracy in our solution. Moreover, a semi-Monte-Carlo simulation is also presented in comparison with the two semi-closed-form pricing formulas. Finally, the effect of incorporating jump and regime switching on the strike price is investigated via numerical analysis.
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43

Liu, Shican, Yu Yang, Hu Zhang, and Yonghong Wu. "Variance Swap Pricing under Markov-Modulated Jump-Diffusion Model." Discrete Dynamics in Nature and Society 2021 (January 8, 2021): 1–16. http://dx.doi.org/10.1155/2021/9814605.

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This paper investigates the pricing of discretely sampled variance swaps under a Markov regime-switching jump-diffusion model. The jump diffusion, as well as other parameters of the underlying stock’s dynamics, is modulated by a Markov chain representing different states of the market. A semi-closed-form pricing formula is derived by applying the generalized Fourier transform method. The counterpart pricing formula for a variance swap with continuous sampling times is also derived and compared with the discrete price to show the improvement of accuracy in our solution. Moreover, a semi-Monte-Carlo simulation is also presented in comparison with the two semi-closed-form pricing formulas. Finally, the effect of incorporating jump and regime switching on the strike price is investigated via numerical analysis.
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44

Makate, Nonthiya, and Pairote Sattayatham. "Stochastic Volatility Jump-Diffusion Model for Option Pricing." Journal of Mathematical Finance 01, no. 03 (2011): 90–97. http://dx.doi.org/10.4236/jmf.2011.13012.

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45

Kostrzewski, Maciej. "Bayesian Inference for the Jump-Diffusion Model withMJumps." Communications in Statistics - Theory and Methods 43, no. 18 (August 20, 2014): 3955–85. http://dx.doi.org/10.1080/03610926.2012.755202.

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46

Zhou, Likai. "Double-smoothed drift estimation of jump-diffusion model." Communications in Statistics - Theory and Methods 46, no. 8 (May 13, 2016): 4137–49. http://dx.doi.org/10.1080/03610926.2015.1078479.

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47

Chakrabarty, Anindya, Zongwei Luo, Rameshwar Dubey, and Shan Jiang. "A theoretical model of jump diffusion-mean reversion." Business Process Management Journal 23, no. 3 (June 5, 2017): 537–54. http://dx.doi.org/10.1108/bpmj-01-2016-0005.

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Purpose The purpose of this paper is to develop a theoretical model of a jump diffusion-mean reversion constant proportion portfolio insurance strategy under the presence of transaction cost and stochastic floor as opposed to the deterministic floor used in the previous literatures. Design/methodology/approach The paper adopts Merton’s jump diffusion (JD) model to simulate the price path followed by risky assets and the CIR mean reversion model to simulate the path followed by the short-term interest rate. The floor of the CPPI strategy is linked to the stochastic process driving the value of a fixed income instrument whose yield follows the CIR mean reversion model. The developed model is benchmarked against CNX-NIFTY 50 and is back tested during the extreme regimes in the Indian market using the scenario-based Monte Carlo simulation technique. Findings Back testing the algorithm using Monte Carlo simulation across the crisis and recovery phases of the 2008 recession regime revealed that the portfolio performs better than the risky markets during the crisis by hedging the downside risk effectively and performs better than the fixed income instruments during the growth phase by leveraging on the upside potential. This makes it a value-enhancing proposition for the risk-averse investors. Originality/value The study modifies the CPPI algorithm by re-defining the floor of the algorithm to be a stochastic mean reverting process which is guided by the movement of the short-term interest rate in the economy. This development is more relevant for two reasons: first, the short-term interest rate changes with time, and hence the constant yield during each rebalancing steps is not practically feasible; second, the historical literatures have revealed that the short-term interest rate tends to move opposite to that of the equity market. Thereby, during the bear run the floor will increase at a higher rate, whereas the growth of the floor will stagnate during the bull phase which aids the model to capitalize on the upward potential during the growth phase and to cut down on the exposure during the crisis phase.
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48

Crosby, John. "A multi-factor jump-diffusion model for commodities†." Quantitative Finance 8, no. 2 (March 2008): 181–200. http://dx.doi.org/10.1080/14697680701253021.

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49

Steinruecke, L., R. Zagst, and A. Swishchuk. "The Markov-switching jump diffusion LIBOR market model." Quantitative Finance 15, no. 3 (October 15, 2014): 455–76. http://dx.doi.org/10.1080/14697688.2014.962594.

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50

Perry, David, and Wolfgang Stadje. "EXACT DISTRIBUTIONS IN A JUMP-DIFFUSION STORAGE MODEL." Probability in the Engineering and Informational Sciences 16, no. 1 (January 2002): 19–27. http://dx.doi.org/10.1017/s026996480216102x.

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We consider a reflected independent superposition of a Brownian motion and a compound Poisson process with positive and negative jumps, which can be interpreted as a model for the content process of a storage system with different types of customers under heavy traffic. The distributions of the duration of a busy cycle and the maximum content during a cycle are determined in closed form.
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