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Journal articles on the topic 'Diffusions affines'

Author: Grafiati

Published: 8 February 2025

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1

Kelly, Leah, Eckhard Platen, and Michael Sørensen. "Estimation for discretely observed diffusions using transform functions." Journal of Applied Probability 41, A (2004): 99–118. http://dx.doi.org/10.1239/jap/1082552193.

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This paper introduces a new estimation technique for discretely observed diffusion processes. Transform functions are applied to transform the data to obtain good and easily calculated estimators of both the drift and diffusion coefficients. Consistency and asymptotic normality of the resulting estimators is investigated. Power transforms are used to estimate the parameters of affine diffusions, for which explicit estimators are obtained.

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2

Kelly, Leah, Eckhard Platen, and Michael Sørensen. "Estimation for discretely observed diffusions using transform functions." Journal of Applied Probability 41, A (2004): 99–118. http://dx.doi.org/10.1017/s0021900200112239.

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This paper introduces a new estimation technique for discretely observed diffusion processes. Transform functions are applied to transform the data to obtain good and easily calculated estimators of both the drift and diffusion coefficients. Consistency and asymptotic normality of the resulting estimators is investigated. Power transforms are used to estimate the parameters of affine diffusions, for which explicit estimators are obtained.

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3

Linetsky, Vadim. "On the transition densities for reflected diffusions." Advances in Applied Probability 37, no. 2 (June 2005): 435–60. http://dx.doi.org/10.1239/aap/1118858633.

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Diffusion models in economics, finance, queueing, mathematical biology, and electrical engineering often involve reflecting barriers. In this paper, we study the analytical representation of transition densities for reflected one-dimensional diffusions in terms of their associated Sturm-Liouville spectral expansions. In particular, we provide explicit analytical expressions for transition densities of Brownian motion with drift, the Ornstein-Uhlenbeck process, and affine (square-root) diffusion with one or two reflecting barriers. The results are easily implementable on a personal computer and should prove useful in applications.

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4

Linetsky, Vadim. "On the transition densities for reflected diffusions." Advances in Applied Probability 37, no. 02 (June 2005): 435–60. http://dx.doi.org/10.1017/s0001867800000252.

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Diffusion models in economics, finance, queueing, mathematical biology, and electrical engineering often involve reflecting barriers. In this paper, we study the analytical representation of transition densities for reflected one-dimensional diffusions in terms of their associated Sturm-Liouville spectral expansions. In particular, we provide explicit analytical expressions for transition densities of Brownian motion with drift, the Ornstein-Uhlenbeck process, and affine (square-root) diffusion with one or two reflecting barriers. The results are easily implementable on a personal computer and should prove useful in applications.

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5

Spreij, Peter, and Enno Veerman. "Affine Diffusions with Non-Canonical State Space." Stochastic Analysis and Applications 30, no. 4 (July 2012): 605–41. http://dx.doi.org/10.1080/07362994.2012.684322.

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6

DAUMAIL, LAURENT, and PATRICK FLORCHINGER. "A CONSTRUCTIVE EXTENSION OF ARTSTEIN'S THEOREM TO THE STOCHASTIC CONTEXT." Stochastics and Dynamics 02, no. 02 (June 2002): 251–63. http://dx.doi.org/10.1142/s0219493702000418.

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The aim of this paper is to extend Artstein's theorem on the stabilization of affine in the control nonlinear deterministic systems to nonlinear stochastic differential systems when both the drift and the diffusion terms are affine in the control. We prove that the existence of a smooth control Lyapunov function implies smooth stabilizability.

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7

Jin, Danqi, Jie Chen, Cedric Richard, Jingdong Chen, and Ali H. Sayed. "Affine Combination of Diffusion Strategies Over Networks." IEEE Transactions on Signal Processing 68 (2020): 2087–104. http://dx.doi.org/10.1109/tsp.2020.2975346.

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8

Glasserman, Paul, and Kyoung-Kuk Kim. "Saddlepoint approximations for affine jump-diffusion models." Journal of Economic Dynamics and Control 33, no. 1 (January 2009): 15–36. http://dx.doi.org/10.1016/j.jedc.2008.04.007.

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9

Hao, Lei, Yali Huang, Yuehua Gao, Xiaoxi Chen, and Peiguang Wang. "Nonrigid Registration of Prostate Diffusion-Weighted MRI." Journal of Healthcare Engineering 2017 (2017): 1–12. http://dx.doi.org/10.1155/2017/9296354.

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Motion and deformation are common in prostate diffusion-weighted magnetic resonance imaging (DWI) during acquisition. These misalignments lead to errors in estimating an apparent diffusion coefficient (ADC) map fitted with DWI. To address this problem, we propose an image registration algorithm to align the prostate DWI and improve ADC map. First, we apply affine transformation to DWI to correct intraslice motions. Then, nonrigid registration based on free-form deformation (FFD) is used to compensate for intraimage deformations. To evaluate the influence of the proposed algorithm on ADC values, we perform statistical experiments in three schemes: no processing of the DWI, with the affine transform approach, and with FFD. The experimental results show that our proposed algorithm can correct the misalignment of prostate DWI and decrease the artifacts of ROI in the ADC maps. These ADC maps thus obtain sharper contours of lesions, which are helpful for improving the diagnosis and clinical staging of prostate cancer.

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10

Duffie, Darrell, Jun Pan, and Kenneth Singleton. "Transform Analysis and Asset Pricing for Affine Jump-diffusions." Econometrica 68, no. 6 (November 2000): 1343–76. http://dx.doi.org/10.1111/1468-0262.00164.

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11

Barletta, Andrea, and Elisa Nicolato. "Orthogonal expansions for VIX options under affine jump diffusions." Quantitative Finance 18, no. 6 (October 5, 2017): 951–67. http://dx.doi.org/10.1080/14697688.2017.1371322.

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12

Ahlip, Rehez, Laurence A. F. Park, Ante Prodan, and Stephen Weissenhofer. "Forward start options under Heston affine jump-diffusions and stochastic interest rate." International Journal of Financial Engineering 08, no. 01 (March 2021): 2150005. http://dx.doi.org/10.1142/s2424786321500055.

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This paper presents a generalization of forward start options under jump diffusion framework of Duffie et al. [Duffie, D, J Pan and K Singleton (2000). Transform analysis and asset pricing for affine jump-diffusions, Econometrica 68, 1343–1376.]. We assume, in addition, the short-term rate is governed by the CIR dynamics introduced in Cox et al. [Cox, JC, JE Ingersoll and SA Ross (1985). A theory of term structure of interest rates, Econometrica 53, 385–408.]. The instantaneous volatilities are correlated with the dynamics of the stock price process, whereas the short-term rate is assumed to be independent of the dynamics of the price process and its volatility. The main result furnishes a semi-analytical formula for the price of the Forward Start European call option. It is derived using probabilistic approach combined with the Fourier inversion technique, as developed in Ahlip and Rutkowski [Ahlip, R and M Rutkowski (2014). Forward start foreign exchange options under Heston’s volatility and CIR interest rates, Inspired By Finance Springer, pp. 1–27], Carr and Madan [Carr, P and D Madan (1999). Option valuation using the fast Fourier transform, Journal of Computational Finance 2, 61–73, Carr, P and D Madan (2009). Saddle point methods for option pricing, Journal of Computational Finance 13, 49–61] as well as Levendorskiĩ [Levendorskiĩ, S (2012). Efficient pricing and reliable calibration in the Heston model, International Journal of Applied Finance 15, 1250050].

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13

Kant, Rama. "Diffusion-Limited Reaction Rates on Self-Affine Fractals." Journal of Physical Chemistry B 101, no. 19 (May 1997): 3781–87. http://dx.doi.org/10.1021/jp963141p.

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14

Li, Lingfei, Rafael Mendoza-Arriaga, and Daniel Mitchell. "Analytical representations for the basic affine jump diffusion." Operations Research Letters 44, no. 1 (January 2016): 121–28. http://dx.doi.org/10.1016/j.orl.2015.12.003.

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15

Filipović, Damir, Eberhard Mayerhofer, and Paul Schneider. "Density approximations for multivariate affine jump-diffusion processes." Journal of Econometrics 176, no. 2 (October 2013): 93–111. http://dx.doi.org/10.1016/j.jeconom.2012.12.003.

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16

Yoo, J. W., I. S. Song, J. W. Shin, and P. G. Park. "A variable step-size diffusion affine projection algorithm." International Journal of Communication Systems 29, no. 5 (July 27, 2015): 1012–25. http://dx.doi.org/10.1002/dac.3015.

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17

Ignatieva, Katja, and Patrick Wong. "Modelling high frequency crude oil dynamics using affine and non-affine jump–diffusion models." Energy Economics 108 (April 2022): 105873. http://dx.doi.org/10.1016/j.eneco.2022.105873.

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18

Adithya B. and Santhi G. "A DNA Sequencing Medical Image Encryption System (DMIES) Using Chaos Map and Knight's Travel Map." International Journal of Reliable and Quality E-Healthcare 11, no. 4 (October 1, 2022): 1–22. http://dx.doi.org/10.4018/ijrqeh.308803.

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This research aims to devise a method of encrypting medical images based on chaos map, Knight's travel map, affine transformation, and DNA cryptography to prevent attackers from accessing the data. The proposed DMIES cryptographic system performs the chaos intertwining logistic map diffusion and confusion process on chosen pixels of medical images. The DNA structure of the medical image has generated using all eight DNA encoding rules that are dependent on the pixel positions in the medical image. Knight's travel map is decomposed, which helps to prevent tampering and certification after the diffusion process. Finally, to avoid the deformity of medical data, a shear-based affine transformation is used. Compared to existing standard image encryption systems, the extensive and complete security assessment highlights the relevance and benefits of the proposed DMIES cryptosystem. The proposed DMIES can also withstand various attacks like statistical, differential, exhaustive, cropping, and noise attack.

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19

CHU, CHI CHIU, and YUE KUEN KWOK. "VALUATION OF GUARANTEED ANNUITY OPTIONS IN AFFINE TERM STRUCTURE MODELS." International Journal of Theoretical and Applied Finance 10, no. 02 (March 2007): 363–87. http://dx.doi.org/10.1142/s0219024907004160.

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We propose three analytic approximation methods for numerical valuation of the guaranteed annuity options in deferred annuity pension policies. The approximation methods include the stochastic duration approach, Edgeworth expansion, and analytic approximation in affine diffusions. The payoff structure in the annuity policies is similar to a quanto call option written on a coupon-bearing bond. To circumvent the limitations of the one-factor interest rate model, we model the interest rate dynamics by a two-factor affine interest rate term structure model. The numerical accuracy and the computational efficiency of these approximation methods are analyzed. We also investigate the value sensitivity of the guaranteed annuity option with respect to different parameters in the pricing model.

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20

Li, Tianyou, Sipei Zhao, Kai Chen, and Jing Lu. "A diffusion filtered-x affine projection algorithm for distributed active noise control." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 268, no. 5 (November 30, 2023): 3050–57. http://dx.doi.org/10.3397/in_2023_0441.

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The well-known Filtered-x Affine Projection (FxAP) algorithm is usually deemed a better choice than the conventional Filtered-x Least-Mean-Square (FxLMS) algorithm when faster convergence speed is desired in active noise control applications. However, the improvement of its convergence performance is obtained at the expense of increased computational complexity. It is usually unrealistic to regulate multichannel ANC systems using the centralized AP algorithm. Recently, distributed diffusion adaptation schemes over acoustic sensor and actuator networks have been introduced to multichannel ANC systems, such as the Diffusion FxLMS algorithms. Distributed processing based on diffusion cooperation strategy allocates the computation load to the network nodes in a scalable manner. This paper proposes a distributed Diffusion Filtered-x AP (DFxAP) algorithm for multichannel ANC systems. Simulation results and computational complexity analysis show that the DFxAP algorithm outperforms the Diffusion FxLMS algorithm in convergence performance and has lower computational complexity compared to the centralized AP algorithm.

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21

da Silva, Allan Jonathan, and Jack Baczynski. "Discretely Distributed Scheduled Jumps and Interest Rate Derivatives: Pricing in the Context of Central Bank Actions." Economies 12, no. 3 (March 19, 2024): 73. http://dx.doi.org/10.3390/economies12030073.

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Interest rate dynamics are influenced by various economic factors, and central bank meetings play a crucial role concerning this subject matter. This study introduces a novel approach to modeling interest rates, focusing on the impact of central banks’ scheduled interventions and their implications for pricing bonds and path-dependent derivatives. We utilize a modified Skellam probability distribution to address the discrete nature of scheduled interest rate jumps and combine them with affine jump-diffusions (AJDs) in order to realistically represent interest rates. We name this class the AJD–Skellam models. Within this class, we provide closed-form formulas for the characteristic functions of a still broad class of interest rate models. The AJD–Skellam models are well-suited for using the interest rate version of the Fourier-cosine series (COS) method for fast and efficient interest rate derivative pricing. Our methodology incorporates this method. The results obtained in the paper demonstrate enhanced accuracy in capturing market behaviors and in pricing interest rate products compared to traditional diffusion models with random jumps. Furthermore, we highlight the applicability of the model to risk management and its potential for broader financial analysis.

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22

Gapeev, Pavel V., and Yavor I. Stoev. "On the construction of non-affine jump-diffusion models." Stochastic Analysis and Applications 35, no. 5 (June 30, 2017): 900–918. http://dx.doi.org/10.1080/07362994.2017.1333008.

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23

Kang, Wanmo, and Chulmin Kang. "Large deviations for affine diffusion processes onR+m×Rn." Stochastic Processes and their Applications 124, no. 6 (June 2014): 2188–227. http://dx.doi.org/10.1016/j.spa.2014.02.002.

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24

Sharifi-Viand, Ahmad, Mohammad Ghasem Mahjani, Reza Moshrefi, and Majid Jafarian. "Diffusion through the self-affine surface of polypyrrole film." Vacuum 114 (April 2015): 17–20. http://dx.doi.org/10.1016/j.vacuum.2014.12.030.

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25

Glasserman, Paul, and Kyoung-Kuk Kim. "MOMENT EXPLOSIONS AND STATIONARY DISTRIBUTIONS IN AFFINE DIFFUSION MODELS." Mathematical Finance 20, no. 1 (January 2010): 1–33. http://dx.doi.org/10.1111/j.1467-9965.2009.00387.x.

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26

Hegger, Rainer, and Peter Grassberger. "Is Diffusion Limited Aggregation Locally Isotropic or Self-Affine?" Physical Review Letters 73, no. 12 (September 19, 1994): 1672–74. http://dx.doi.org/10.1103/physrevlett.73.1672.

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27

Modalavalasa, Sowjanya, Upendra Kumar Sahoo, and Ajit Kumar Sahoo. "Diffusion minimum Wilcoxon affine projection algorithm over distributed networks." Digital Signal Processing 109 (February 2021): 102918. http://dx.doi.org/10.1016/j.dsp.2020.102918.

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28

Friesen, Martin, Peng Jin, Jonas Kremer, and Barbara Rüdiger. "Ergodicity of affine processes on the cone of symmetric positive semidefinite matrices." Advances in Applied Probability 52, no. 3 (September 2020): 825–54. http://dx.doi.org/10.1017/apr.2020.21.

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AbstractThis article investigates the long-time behavior of conservative affine processes on the cone of symmetric positive semidefinite $d\times d$ matrices. In particular, for conservative and subcritical affine processes we show that a finite $\log$ -moment of the state-independent jump measure is sufficient for the existence of a unique limit distribution. Moreover, we study the convergence rate of the underlying transition kernel to the limit distribution: first, in a specific metric induced by the Laplace transform, and second, in the Wasserstein distance under a first moment assumption imposed on the state-independent jump measure and an additional condition on the diffusion parameter.

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29

Tappe, Stefan. "Existence of affine realizations for Lévy term structure models." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2147 (June 27, 2012): 3685–704. http://dx.doi.org/10.1098/rspa.2012.0089.

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We investigate the existence of affine realizations for term structure models driven by Lévy processes. It turns out that we obtain more severe restrictions on the volatility than in the classical diffusion case without jumps. As special cases, we study constant direction volatilities and the existence of short-rate realizations.

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30

FRAME, SAMUEL J., and CYRUS A. RAMEZANI. "BAYESIAN ESTIMATION OF ASYMMETRIC JUMP-DIFFUSION PROCESSES." Annals of Financial Economics 09, no. 03 (December 2014): 1450008. http://dx.doi.org/10.1142/s2010495214500080.

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The hypothesis that asset returns are normally distributed has been widely rejected. The literature has shown that empirical asset returns are highly skewed and leptokurtic. The affine jump-diffusion (AJD) model improves upon the normal specification by adding a jump component to the price process. Two important extensions proposed by Ramezani and Zeng (1998) and Kou (2002) further improve the AJD specification by having two jump components in the price process, resulting in the asymmetric affine jump-diffusion (AAJD) specification. The AAJD specification allows the probability distribution of the returns to be asymmetrical. That is, the tails of the distribution are allowed to have different shapes and densities. The empirical literature on the "leverage effect" shows that the impact of innovations in prices on volatility is asymmetric: declines in stock prices are accompanied by larger increases in volatility than the reverse. The asymmetry in AAJD specification indirectly accounts for the leverage effect and is therefore more consistent with the empirical distributions of asset returns. As a result, the AAJD specification has been widely adopted in the portfolio choice, option pricing, and other branches of the literature. However, because of their complexity, empirical estimation of the AAJD models has received little attention to date. The primary objective of this paper is to contribute to the econometric methods for estimating the parameters of the AAJD models. Specifically, we develop a Bayesian estimation technique. We provide a comparison of the estimated parameters under the Bayesian and maximum likelihood estimation (MLE) methodologies using the S&P 500, the NASDAQ, and selected individual stocks. Focusing on the most recent spectacular market bust (2007–2009) and boom (2009–2010) periods, we examine how the parameter estimates differ under distinctly different economic conditions.

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31

Kengnou Telem, Adélaïde Nicole, Cyrille Feudjio, Balamurali Ramakrishnan, Hilaire Bertrand Fotsin, and Karthikeyan Rajagopal. "A Simple Image Encryption Based on Binary Image Affine Transformation and Zigzag Process." Complexity 2022 (January 7, 2022): 1–22. http://dx.doi.org/10.1155/2022/3865820.

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In this paper, we propose a new and simple method for image encryption. It uses an external secret key of 128 bits long and an internal secret key. The novelties of the proposed encryption process are the methods used to extract an internal key to apply the zigzag process, affine transformation, and substitution-diffusion process. Initially, an original gray-scale image is converted into binary images. An internal secret key is extracted from binary images. The two keys are combined to compute the substitution-diffusion keys. The zigzag process is firstly applied on each binary image. Using an external key, every zigzag binary image is reflected or rotated and a new gray-scale image is reconstructed. The new image is divided into many nonoverlapping subblocks, and each subblock uses its own key to take out a substitution-diffusion process. We tested our algorithms on many biomedical and nonmedical images. It is seen from evaluation metrics that the proposed image encryption scheme provides good statistical and diffusion properties and can resist many kinds of attacks. It is an efficient and secure scheme for real-time encryption and transmission of biomedical images in telemedicine.

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32

Gourieroux, C. "A Classification of Two-Factor Affine Diffusion Term Structure Models." Journal of Financial Econometrics 4, no. 1 (August 19, 2005): 31–52. http://dx.doi.org/10.1093/jjfinec/nbj003.

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33

Nunes, João Pedro Vidal, and Tiago Ramalho Viegas Alcaria. "Valuation of forward start options under affine jump-diffusion models." Quantitative Finance 16, no. 5 (July 31, 2015): 727–47. http://dx.doi.org/10.1080/14697688.2015.1049200.

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34

Fernandez-Bes, Jesus, Luis A. Azpicueta-Ruiz, Jerónimo Arenas-García, and Magno T. M. Silva. "Distributed estimation in diffusion networks using affine least-squares combiners." Digital Signal Processing 36 (January 2015): 1–14. http://dx.doi.org/10.1016/j.dsp.2014.09.004.

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35

Yun, Jaeho. "Out-of-sample density forecasts with affine jump diffusion models." Journal of Banking & Finance 47 (October 2014): 74–87. http://dx.doi.org/10.1016/j.jbankfin.2014.06.024.

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36

Florchinger, Patrick. "A Jurdjevic-Quinn theorem for stochastic differential systems under weak conditions." Control and Cybernetics 51, no. 1 (March 1, 2022): 21–29. http://dx.doi.org/10.2478/candc-2022-0002.

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Abstract The purpose of this paper is to provide sufficient conditions for the stabilizability of weak solutions of stochastic differential systems when both the drift and diffusion are affine in the control. This result extends the well–known theorem of Jurdjevic– Quinn (Jurdjevic and Quinn, 1978) to stochastic differential systems under weaker conditions on the system coefficients than those assumed in Florchinger (2002).

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37

Avram, Florin, and Miguel Usabel. "The Gerber-shiu Expected Discounted Penalty-reward Function under an Affine Jump-diffusion Model." ASTIN Bulletin 38, no. 2 (November 2004): 461–81. http://dx.doi.org/10.1017/s0515036100015257.

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We provide a unified analytical treatment of first passage problems under an affine state-dependent jump-diffusion model (with drift and volatility depending linearly on the state). Our proposed model, that generalizes several previously studied cases, may be used for example for obtaining probabilities of ruin in the presence of interest rates under the rational investement strategies proposed by Berk & Green (2004).

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38

Avram, Florin, and Miguel Usabel. "The Gerber-shiu Expected Discounted Penalty-reward Function under an Affine Jump-diffusion Model." ASTIN Bulletin 38, no. 02 (November 2008): 461–81. http://dx.doi.org/10.2143/ast.38.2.2033350.

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We provide a unified analytical treatment of first passage problems under an affine state-dependent jump-diffusion model (with drift and volatility depending linearly on the state). Our proposed model, that generalizes several previously studied cases, may be used for example for obtaining probabilities of ruin in the presence of interest rates under the rational investement strategies proposed by Berk & Green (2004).

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39

Nautiyal, Mayank, Sankha Subhra Bhattacharjee, and Nithin V. George. "Low Complexity and Robust Diffusion Affine Projection Algorithms for Distributed Estimation." IEEE Transactions on Circuits and Systems II: Express Briefs 69, no. 3 (March 2022): 1952–56. http://dx.doi.org/10.1109/tcsii.2021.3127464.

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40

Alghunaim, Sulaiman A., Kun Yuan, and Ali H. Sayed. "A Proximal Diffusion Strategy for Multiagent Optimization With Sparse Affine Constraints." IEEE Transactions on Automatic Control 65, no. 11 (November 2020): 4554–67. http://dx.doi.org/10.1109/tac.2019.2960265.

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41

Broadie, Mark, and Özgür Kaya. "Exact Simulation of Stochastic Volatility and Other Affine Jump Diffusion Processes." Operations Research 54, no. 2 (April 2006): 217–31. http://dx.doi.org/10.1287/opre.1050.0247.

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42

Nomikos, N. K., and O. Soldatos. "Using Affine Jump Diffusion Models for Modelling and Pricing Electricity Derivatives." Applied Mathematical Finance 15, no. 1 (February 2008): 41–71. http://dx.doi.org/10.1080/13504860701427362.

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43

Song, Pucha, Haiquan Zhao, Pengfei Li, and Long Shi. "Diffusion affine projection maximum correntropy criterion algorithm and its performance analysis." Signal Processing 181 (April 2021): 107918. http://dx.doi.org/10.1016/j.sigpro.2020.107918.

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44

Kim, Kyoung-Kuk. "Stability analysis of Riccati differential equations related to affine diffusion processes." Journal of Mathematical Analysis and Applications 364, no. 1 (April 2010): 18–31. http://dx.doi.org/10.1016/j.jmaa.2009.11.020.

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45

Hu, Limei, Feng Chen, Shukai Duan, Lidan Wang, and Jiagui Wu. "An Improved Diffusion Affine Projection Estimation Algorithm for Wireless Sensor Networks." Circuits, Systems, and Signal Processing 39, no. 6 (December 5, 2019): 3173–88. http://dx.doi.org/10.1007/s00034-019-01317-5.

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46

Barabási, Albert-László, and Tamás Vicsek. "Tracing a diffusion-limited aggregate: Self-affine versus self-similar scaling." Physical Review A 41, no. 12 (June 1, 1990): 6881–83. http://dx.doi.org/10.1103/physreva.41.6881.

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47

Steffensen, Mogens. "Quadratic Optimization of Life and Pension Insurance Payments." ASTIN Bulletin 36, no. 01 (May 2006): 245–67. http://dx.doi.org/10.2143/ast.36.1.2014151.

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Quadratic optimization is the classical approach to optimal control of pension funds. Usually the payment stream is approximated by a diffusion process. Here we obtain semiexplicit solutions for quadratic optimization in the case where the payment process is driven by a finite state Markov chain model commonly used in life insurance mathematics. The optimal payments are affine in the surplus with state dependent coefficients. Also constraints on payments and surplus are studied.

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48

Steffensen, Mogens. "Quadratic Optimization of Life and Pension Insurance Payments." ASTIN Bulletin 36, no. 1 (May 2006): 245–67. http://dx.doi.org/10.1017/s0515036100014471.

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Quadratic optimization is the classical approach to optimal control of pension funds. Usually the payment stream is approximated by a diffusion process. Here we obtain semiexplicit solutions for quadratic optimization in the case where the payment process is driven by a finite state Markov chain model commonly used in life insurance mathematics. The optimal payments are affine in the surplus with state dependent coefficients. Also constraints on payments and surplus are studied.

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49

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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Bolyog, Beáta, and Gyula Pap. "On conditional least squares estimation for affine diffusions based on continuous time observations." Statistical Inference for Stochastic Processes 22, no. 1 (February 5, 2018): 41–75. http://dx.doi.org/10.1007/s11203-018-9174-z.

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