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McMurray, Eamon Finnian Valentine. "Regularity of McKean-Vlasov stochastic differential equations and applications". Thesis, Imperial College London, 2015. http://hdl.handle.net/10044/1/28918.
Pełny tekst źródłaMezerdi, Mohamed Amine. "Equations différentielles stochastiques de type McKean-Vlasov et leur contrôle optimal". Electronic Thesis or Diss., Toulon, 2020. http://www.theses.fr/2020TOUL0014.
Pełny tekst źródłaWe consider Mc Kean-Vlasov stochastic differential equations (SDEs), which are SDEs where the drift and diffusion coefficients depend not only on the state of the unknown process but also on its probability distribution. These SDEs called also mean- field SDEs were first studied in statistical physics and represent in some sense the average behavior of an infinite number of particles. Recently there has been a renewed interest for this kind of equations in the context of mean-field game theory. Since the pioneering papers by P.L. Lions and J.M. Lasry, mean-field games and mean-field control theory has raised a lot of interest, motivated by applications to various fields such as game theory, mathematical finance, communications networks and management of oil resources. In this thesis, we studied questions of stability with respect to initial data, coefficients and driving processes of Mc Kean-Vlasov equations. Generic properties for this type of SDEs, such as existence and uniqueness, stability with respect to parameters, have been investigated. In control theory, our attention were focused on existence, approximation of relaxed controls for controlled Mc Kean-Vlasov SDEs
Izydorczyk, Lucas. "Probabilistic backward McKean numerical methods for PDEs and one application to energy management". Electronic Thesis or Diss., Institut polytechnique de Paris, 2021. http://www.theses.fr/2021IPPAE008.
Pełny tekst źródłaThis thesis concerns McKean Stochastic Differential Equations (SDEs) to representpossibly non-linear Partial Differential Equations (PDEs). Those depend not onlyon the time and position of a given particle, but also on its probability law. In particular, we treat the unusual case of Fokker-Planck type PDEs with prescribed final data. We discuss existence and uniqueness for those equations and provide a probabilistic representation in the form of McKean type equation, whose unique solution corresponds to the time-reversal dynamics of a diffusion process.We introduce the notion of fully backward representation of a semilinear PDE: thatconsists in fact in the coupling of a classical Backward SDE with an underlying processevolving backwardly in time. We also discuss an application to the representationof Hamilton-Jacobi-Bellman Equation (HJB) in stochastic control. Based on this, we propose a Monte-Carlo algorithm to solve some control problems which has advantages in terms of computational efficiency and memory whencompared to traditional forward-backward approaches. We apply this method in the context of demand side management problems occurring in power systems. Finally, we survey the use of generalized McKean SDEs to represent non-linear and non-conservative extensions of Fokker-Planck type PDEs
Le, cavil Anthony. "Représentation probabiliste de type progressif d'EDP nonlinéaires nonconservatives et algorithmes particulaires". Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLY023.
Pełny tekst źródłaThis thesis performs forward probabilistic representations of nonlinear and nonconservative Partial Differential Equations (PDEs), which allowto numerically estimate the corresponding solutions via an interacting particle system algorithm, mixing Monte-Carlo methods and non-parametric density estimates.In the literature, McKean typeNonlinear Stochastic Differential Equations (NLSDEs) constitute the microscopic modelof a class of PDEs which are conservative. The solution of a NLSDEis generally a couple $(Y,u)$ where $Y$ is a stochastic process solving a stochastic differential equation whose coefficients depend on $u$ and at each time $t$, $u(t,cdot)$ is the law density of the random variable $Y_t$.The main idea of this thesis is to consider this time a non-conservative PDE which is the result of a conservative PDE perturbed by a term of the type $Lambda(u, nabla u) u$. In this case, the solution of the corresponding NLSDE is again a couple $(Y,u)$, where again $Y$ is a stochastic processbut where the link between the function $u$ and $Y$ is more complicated and once fixed the law of $Y$, $u$ is determined by a fixed pointargument via an innovating Feynmann-Kac type formula
Le, cavil Anthony. "Représentation probabiliste de type progressif d'EDP nonlinéaires nonconservatives et algorithmes particulaires". Electronic Thesis or Diss., Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLY023.
Pełny tekst źródłaThis thesis performs forward probabilistic representations of nonlinear and nonconservative Partial Differential Equations (PDEs), which allowto numerically estimate the corresponding solutions via an interacting particle system algorithm, mixing Monte-Carlo methods and non-parametric density estimates.In the literature, McKean typeNonlinear Stochastic Differential Equations (NLSDEs) constitute the microscopic modelof a class of PDEs which are conservative. The solution of a NLSDEis generally a couple (Y,u) where Y is a stochastic process solving a stochastic differential equation whose coefficients depend on u and at each time t, u(t,.) is the law density of the random variable Yt.The main idea of this thesis is to consider this time a non-conservative PDE which is the result of a conservative PDE perturbed by a term of the type Lambda(u, nabla u) u. In this case, the solution of the corresponding NLSDE is again a couple (Y,u), where again Y is a stochastic processbut where the link between the function u and Y is more complicated and once fixed the law of Y, u is determined by a fixed pointargument via an innovating Feynmann-Kac type formula
Treacy, Brian. "A stochastic differential equation derived from evolutionary game theory". Thesis, Uppsala universitet, Analys och sannolikhetsteori, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-377554.
Pełny tekst źródłaAl-Saadony, Muhannad. "Bayesian stochastic differential equation modelling with application to finance". Thesis, University of Plymouth, 2013. http://hdl.handle.net/10026.1/1530.
Pełny tekst źródłaLi, Shuang. "Study of Various Stochastic Differential Equation Models for Finance". Thesis, Curtin University, 2017. http://hdl.handle.net/20.500.11937/56545.
Pełny tekst źródłaBotha, Imke. "Bayesian inference for stochastic differential equation mixed effects models". Thesis, Queensland University of Technology, 2020. https://eprints.qut.edu.au/198039/1/Imke_Botha_Thesis.pdf.
Pełny tekst źródłaZararsiz, Zarife. "On an epidemic model given by a stochastic differential equation". Thesis, Växjö University, School of Mathematics and Systems Engineering, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-5747.
Pełny tekst źródłaAhmad, Ferhana. "A stochastic partial differential equation approach to mortgage backed securities". Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:ee33aa2d-b9fa-4cc4-a399-5f681966bc77.
Pełny tekst źródłaBrites, Nuno M. "Stochastic differential equation harvesting models: sustainable policies and profit optimization". Doctoral thesis, Universidade de Évora, 2017. http://hdl.handle.net/10174/21965.
Pełny tekst źródłaWang, Yong Tian. "Stochastic differential delay equation with jumps and application to finance". Thesis, Swansea University, 2007. https://cronfa.swan.ac.uk/Record/cronfa43121.
Pełny tekst źródłaZhou, Yanli. "Computational methods for various stochastic differential equation models in finance". Thesis, Curtin University, 2014. http://hdl.handle.net/20.500.11937/247.
Pełny tekst źródłaShedlock, Andrew James. "A Numerical Method for solving the Periodic Burgers' Equation through a Stochastic Differential Equation". Thesis, Virginia Tech, 2021. http://hdl.handle.net/10919/103947.
Pełny tekst źródłaMaster of Science
Burgers equation is a Partial Differential Equation (PDE) used to model how fluids evolve in time based on some initial condition and viscosity parameter. This viscosity parameter helps describe how the energy in a fluid dissipates. When studying partial differential equations, it is often hard to find a closed form solution to the problem, so we often approximate the solution with numerical methods. As our viscosity parameter approaches 0, many numerical methods develop problems and may no longer accurately compute the solution. Using random variables, we develop an approximation algorithm and test our numerical method on various types of initial conditions with small viscosity coefficients.
Xiong, Sheng. "Stochastic Differential Equations: Some Risk and Insurance Applications". Diss., Temple University Libraries, 2011. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/133166.
Pełny tekst źródłaPh.D.
In this dissertation, we have studied diffusion models and their applications in risk theory and insurance. Let Xt be a d-dimensional diffusion process satisfying a system of Stochastic Differential Equations defined on an open set G Rd, and let Ut be a utility function of Xt with U0 = u0. Let T be the first time that Ut reaches a level u^*. We study the Laplace transform of the distribution of T, as well as the probability of ruin, psileft(u_{0}right)=Prleft{ T
Pereira, Lo Bernardino. "Parameter estimation for a stochastic differential equation model of polymer rheology". Thesis, Imperial College London, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.441346.
Pełny tekst źródłaZhao, Lin. "Portfolio selection of stochastic differential equation with jumps under regime switching". Thesis, Swansea University, 2010. https://cronfa.swan.ac.uk/Record/cronfa42401.
Pełny tekst źródłaMesserschmidt, Reinhardt. "Hattendorff’s theorem and Thiele’s differential equation generalized". Diss., University of Pretoria, 2005. http://hdl.handle.net/2263/30476.
Pełny tekst źródłaDissertation (MSc (Actuarial Science))--University of Pretoria, 2007.
Insurance and Actuarial Science
unrestricted
Lemos, Alice Loureiro Leocádio Botelho de. "A study on Thiele's Differential Equation". Master's thesis, Instituto Superior de Economia e Gestão, 2014. http://hdl.handle.net/10400.5/7975.
Pełny tekst źródłaThorvald Nicolai Thiele foi um importante investigador dinamarquês. Entre os seus contributos, destaca-se em particular o facto de ter provado que para um seguro de vida inteira com benefício de valor 1, emitido sobre uma pessoa e pago imediatamente após a morte, as reservas prospetivas satisfazem uma equação diferencial linear: a chamada equação diferencial de Thiele. De um modo mais geral, as equações diferenciais de Thiele são um sistema diferencial linear de equações que descrevem a dinâmica das reservas nos seguros de vida e pensões em tempo contínuo. Este texto tem como principal objetivo rever de forma tão completa quanto possível as contribuições relacionadas com a equação de Thiele que foram surgindo ao longo do tempo, dando assim o presente estado de arte deste relevante tópico. Começando por fazer uma revisão breve do essencial da matemática atuarial avança depois para a derivação da equação de Thiele, considerando os dois modelos de mortalidade, o clássico e o de múltiplos estados, sobre uma pessoa e sobre várias pessoas. Algumas ilustrações, para vários tipos de contrato, são seguidamente introduzidas. Dos desenvolvimentos conhecidos, dá-se especial destaque às generalizações da equação diferencial que incluem um processo estocástico de pagamentos e um processo de difusão para a taxa de juro. Apresenta-se também o uso da equação como ferramenta para o desenvolvimento de produtos de seguro de vida e descreve-se uma generalização da equação diferencial para uma carteira fechada de seguros. A última parte do trabalho faz um resumo de outros contributos relacionados com a equação.
Thiele's differential equation has a long history, dating back to an unpublished note of Thiele, 1875. Thorvald Nicolai Thiele was a Danish researcher who worked as an actuary, astronomer, mathematician and statistician. He proved that for a whole life assurance of a single individual with benefit of amount 1, payable immediately on death, the prospective reserve satisfies a certain linear differential equation, which is extremely useful for the understanding of reality: Thiele's differential equation. In a more general framework, Thiele's differential equations for the prospective reserve are a linear system of differential equations describing the dynamics of reserves in life and pension insurance in continuous time. This text has the main purpose of reviewing in a comprehensive way the contributions related to Thiele's equation that appeared over time, presenting the status of the art on this important topic. A revision of life insurance mathematics is first and then Thiele?s differential equation is derived under the classical and multiple state model of human mortality for one life and for multiple lives After this, some illustrations are presented under different types of contracts. Following the developments in the literature, more general differential equations are obtained, including a stochastic payment process and a diffusion process for interest rate. The technique of using Thiele's differential equation as a tool for life insurance product development and the generalization of the equation for a closed insurance portfolio are also discussed. Finally, other developments are summarised.
Banerjee, Paromita. "Numerical Methods for Stochastic Differential Equations and Postintervention in Structural Equation Models". Case Western Reserve University School of Graduate Studies / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=case1597879378514956.
Pełny tekst źródłaXu, Lina. "Simulation methods for stochastic differential equations in finance". Thesis, Queensland University of Technology, 2019. https://eprints.qut.edu.au/134388/1/Lina_Xu_Thesis.pdf.
Pełny tekst źródłaGrecksch, Wilfried, i Christian Roth. "Approximation of a Quasilinear Stochastic Partial Differential Equation driven by Fractional White Noise". Universitätsbibliothek Chemnitz, 2008. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200800521.
Pełny tekst źródłaLuo, Ye. "Random periodic solutions of stochastic functional differential equations". Thesis, Loughborough University, 2014. https://dspace.lboro.ac.uk/2134/16112.
Pełny tekst źródłaYevik, Andrei. "Numerical approximations to the stationary solutions of stochastic differential equations". Thesis, Loughborough University, 2011. https://dspace.lboro.ac.uk/2134/7777.
Pełny tekst źródłaFantozzi, Marco. "Large deviations for differential stochastic equations with additive noise". Doctoral thesis, Scuola Normale Superiore, 2007. http://hdl.handle.net/11384/85673.
Pełny tekst źródłaAhlip, Rehez Ajmal. "Stability & filtering of stochastic systems". Thesis, Queensland University of Technology, 1997.
Znajdź pełny tekst źródłaWei, Fajin. "Stochastic Infinity-Laplacian equation and One-Laplacian equation in image processing and mean curvature flows : finite and large time behaviours". Thesis, Loughborough University, 2010. https://dspace.lboro.ac.uk/2134/7345.
Pełny tekst źródłaNguyen, Cu Ngoc. "Stochastic differential equations with long-memory input". Thesis, Queensland University of Technology, 2001.
Znajdź pełny tekst źródłaKnani, Habiba. "Backward stochastic differential equations driven by Gaussian Volterra processes". Electronic Thesis or Diss., Université de Lorraine, 2020. http://www.theses.fr/2020LORR0014.
Pełny tekst źródłaThis thesis treats of backward stochastic differential equations (BSDE) driven by a class of Gaussian Volterra processes that includes multifractional Brownian motion and multifractional Ornstein-Uhlenbeck processes. In the first part we study multidimensional BSDE with generators that are linear functions of the solution. By means of an Itoˆ formula for Volterra processes, a linear second order partial differential equation (PDE) with terminal condition is associated to the BSDE. Under an integrability condition on a functional of the second moment of the Volterra process in a neighbourhood of the terminal time, we solve the associated PDE explicitely and deduce the solution of the linear BSDE. We discuss an application in the context of self-financing trading stategies. The second part of the thesis treats of non-linear BSDE driven by the same class of Gaussian Volterra processes. The main results are the existence and uniqueness of the solution in a space of regular functionals of the Volterra process, and a comparison theorem for the solutions of BSDE. We give two proofs for the existence and uniqueness of the solution, one is based on the associated PDE and a second one without making reference to this PDE, but with probabilistic and functional theoretic methods. Especially this second proof is technically quite complex, and, due to the absence of mar- tingale properties in the context of Volterra processes, requires to work with different norms on the underlying Hilbert space that is defined by the kernel of the Volterra process. For the construction of the solution we need the notion of quasi-conditional expectation, a Clark-Ocone type formula and another Itoˆ formula for Volterra processes. Contrary to the more classical cases of BSDE driven by Brownian or fractional Brownian motion, an assumption on the behaviour of the kernel of the driv- ing Volterra process is in general necessary for the wellposedness of the BSDE. For multifractional Brownian motion this assumption is closely related to the behaviour of the Hurst function
Miserocchi, Andrea. "The Fokker-Planck equation as model for the stochastic gradient descent in deep learning". Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/18290/.
Pełny tekst źródłaThomas, Philipp. "Systematic approximation methods for stochastic biochemical kinetics". Thesis, University of Edinburgh, 2015. http://hdl.handle.net/1842/16197.
Pełny tekst źródłaMayo, Nardone Pablo Sabino. "Modeling the Heat Flow Dynamics of a Houses Using Stochastic Differential Equations". Thesis, KTH, Skolan för industriell teknik och management (ITM), 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-302557.
Pełny tekst źródłaDenna forskning syftar till att utforska nya sätt att bedöma energiprestanda inom bostäder. Huvudsyftetmed detta arbete är att föreslå en värmedynamikmodell baserad på övervakningsdata för att bidra till enenergieffektiv övergång inom byggsektorn. En omfattande studie av tillgängliga matematiska och statistiska verktyg beskrivs för att bestämma enhelhetslösning, som finns i gråboxmodeller. Denna modellstrategi ger möjlighet att förstå multivariatasystem, som kan tillämpas på en hushålls värmedynamik. Genom den iterativa processen att testa varje möjlig modell bestämmer detta arbete den med bästförklarande kraft, och definierar de studerade husenhetens termiska egenskaper. Denna metod gör detmöjligt att upptäcka underpresterande bostäder bland anläggningar med hög energieffektivitetsstandard. Denna undersökning återspeglar möjligheten att använda gråboxmodeller för att förutsäga dynamiken ivärmerelaterade system. Dessutom lägger den grunden för nya sätt att använda övervakningsdata förbostäder.
Tempone, Olariaga Raul. "Numerical Complexity Analysis of Weak Approximation of Stochastic Differential Equations". Doctoral thesis, KTH, Numerisk analys och datalogi, NADA, 2002. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3413.
Pełny tekst źródłaQC 20100825
Zhou, Bo. "The existence of bistable stationary solutions of random dynamical systems generated by stochastic differential equations and random difference equations". Thesis, Loughborough University, 2009. https://dspace.lboro.ac.uk/2134/14255.
Pełny tekst źródłaMelichov, Dmitrij. "On estimation of the Hurst index of solutions of stochastic differential equations". Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2011. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2011~D_20111228_165042-00002.
Pełny tekst źródłaPagrindinė šios disertacijos tema – stochastinių diferencialinių lygčių (SDL), valdomų trupmeninio Brauno judesio (tBj), sprendinių Hursto indekso H vertinimas. Pirmiausia disertacijoje išnagrinėta SDL, valdomų tBj, sprendinių pirmos ir antros eilės kvadratinių variacijų ribinė elgsena. Iš šių rezultatų seka keli stipriai pagrįsti Hursto indekso H įvertiniai. Įrodyta, kad šie įvertiniai išlieka stipriai pagrįsti, jei tikra sprendinio trajektorija keičiama jos Milšteino aproksimacija. Taip pat išnagrinėtos pokyčių santykio (increment ratios) statistikos H įvertinio, gauto J. M. Bardeto ir D. Surgailio 2010 m., taikymo trupmeninio geometrinio Brauno judesio Hursto indekso vertinimui galimybės bei nustatytas modifikuoto Gladyševo H įvertinio konvergavimo i tikrąją parametro reikšme greitis. Gauti įvertiniai palyginti su kai kuriais kitais žinomais Hursto indekso H įvertiniais: naiviais bei mažiausių kvadratų Gladyševo ir eta-sumavimo osciliacijos įvertiniais, variogramos įvertiniu ir pokyčių santykio statistikos įvertiniu. Įvertinių elgsena buvo palyginta trupmeniniam Ornšteino-Ulenbeko (OU) procesui bei trupmeniniam geometriniam Brauno judesiui (gBj). Pradinės išvados buvo padarytos O-U procesui, kuris yra Gauso, o gBj procesas buvo naudojamas patikrinti, kaip šie įvertiniai elgiasi, kai procesas yra ne Gauso. Disertaciją sudaro įvadas, 3 pagrindiniai skyriai, išvados, literatūros sąrašas, autoriaus publikacijų disertacijos tema sąrašas ir du priedai.
Redmon, Jessica. "Stochastic Bubble Formation and Behavior in Non-Newtonian Fluids". Case Western Reserve University School of Graduate Studies / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=case15602738261697.
Pełny tekst źródłaMasike, Kakanyo Knowledge. "The required ansatz to construct Lie point transformations and the symmetries of a first-order stochastic differential equation". Master's thesis, University of Cape Town, 2011. http://hdl.handle.net/11427/14145.
Pełny tekst źródłaMcKinley, Scott Alister. "An existence result from the theory of fluctuating hydrodynamics of polymers in dilute solution". Columbus, Ohio : Ohio State University, 2006. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1149020682.
Pełny tekst źródłaWang, Shuo. "Analysis and Application of Haseltine and Rawlings's Hybrid Stochastic Simulation Algorithm". Diss., Virginia Tech, 2016. http://hdl.handle.net/10919/82717.
Pełny tekst źródłaPh. D.
Cormier, Quentin. "Comportement en temps long d'un modèle champ moyen de neurones à décharge en interactions". Thesis, Université Côte d'Azur, 2021. http://www.theses.fr/2021COAZ4008.
Pełny tekst źródłaWe study the long time behavior of a McKean-Vlasov stochastic differential equation (SDE), driven by a Poisson measure. In neuroscience, this SDE models the dynamics of the membrane potential of a typical neuron in a large network. The model can be derived by considering a finite network of generalized Integrate-And-Fire neurons and by taking the limit where the number of neurons goes to infinity. Hence the McKean-Vlasov SDE is a mean-field model of spiking neurons.We study existence and uniqueness of the solution this McKean-Vlasov SDE and describe its invariant probability measures. For small enough interaction parameter J, we prove uniqueness and global stability of the invariant measure. For J arbitrary large however, the invariant measures may not be unique. We give a sufficient condition ensuring the local stability of such a given invariant probability measure. Our criterion involves the location of the zeros of an explicit holomorphic function associated to the considered stationary solution. When all the zeros have negative real part, we prove that stability holds. We then give sufficient general conditions ensuring the existence of periodic solutions through a Hopf bifurcation: at some critical interaction parameter J0, the invariant probability losses its stability and periodic solutions appear for J close to J0. To obtain these results, we combine probabilistic and deterministic methods. In particular, a key tool in this analysis is a nonlinear Volterra Integral equation satisfied by the synaptic current.Finally, we illustrate these results with examples which are tractable analytically. Additionally, we give numerical methods to approximate the solution of the mean-field equation and to predict numerically the bifurcations
Kateregga, Michael. "Perturbation methods in derivatives pricing under stochastic volatility". Thesis, Stellenbosch : Stellenbosch University, 2012. http://hdl.handle.net/10019.1/71708.
Pełny tekst źródłaENGLISH ABSTRACT: This work employs perturbation techniques to price and hedge financial derivatives in a stochastic volatility framework. Fouque et al. [44] model volatility as a function of two processes operating on different time-scales. One process is responsible for the fast-fluctuating feature of volatility and corresponds to the slow time-scale and the second is for slowfluctuations or fast time-scale. The former is an Ergodic Markov process and the latter is a strong solution to a Lipschitz stochastic differential equation. This work mainly involves modelling, analysis and estimation techniques, exploiting the concept of mean reversion of volatility. The approach used is robust in the sense that it does not assume a specific volatility model. Using singular and regular perturbation techniques on the resulting PDE a first-order price correction to Black-Scholes option pricing model is derived. Vital groupings of market parameters are identified and their estimation from market data is extremely efficient and stable. The implied volatility is expressed as a linear (affine) function of log-moneyness-tomaturity ratio, and can be easily calibrated by estimating the grouped market parameters from the observed implied volatility surface. Importantly, the same grouped parameters can be used to price other complex derivatives beyond the European and American options, which include Barrier, Asian, Basket and Forward options. However, this semi-analytic perturbative approach is effective for longer maturities and unstable when pricing is done close to maturity. As a result a more accurate technique, the decomposition pricing approach that gives explicit analytic first- and second-order pricing and implied volatility formulae is discussed as one of the current alternatives. Here, the method is only employed for European options but an extension to other options could be an idea for further research. The only requirements for this method are integrability and regularity of the stochastic volatility process. Corrections to [3] remarkable work are discussed here.
AFRIKAANSE OPSOMMING: Hierdie werk gebruik steuringstegnieke om finansiële afgeleide instrumente in ’n stogastiese wisselvalligheid raamwerk te prys en te verskans. Fouque et al. [44] gemodelleer wisselvalligheid as ’n funksie van twee prosesse wat op verskillende tyd-skale werk. Een proses is verantwoordelik vir die vinnig-wisselende eienskap van die wisselvalligheid en stem ooreen met die stadiger tyd-skaal en die tweede is vir stadig-wisselende fluktuasies of ’n vinniger tyd-skaal. Die voormalige is ’n Ergodiese-Markov-proses en die laasgenoemde is ’n sterk oplossing vir ’n Lipschitz stogastiese differensiaalvergelyking. Hierdie werk behels hoofsaaklik modellering, analise en skattingstegnieke, wat die konsep van terugkeer to die gemiddelde van die wisseling gebruik. Die benadering wat gebruik word is rubuust in die sin dat dit nie ’n aanname van ’n spesifieke wisselvalligheid model maak nie. Deur singulêre en reëlmatige steuringstegnieke te gebruik op die PDV kan ’n eerste-orde pryskorreksie aan die Black-Scholes opsie-waardasiemodel afgelei word. Belangrike groeperings van mark parameters is geïdentifiseer en hul geskatte waardes van mark data is uiters doeltreffend en stabiel. Die geïmpliseerde onbestendigheid word uitgedruk as ’n lineêre (affiene) funksie van die log-geldkarakter-tot-verval verhouding, en kan maklik gekalibreer word deur gegroepeerde mark parameters te beraam van die waargenome geïmpliseerde wisselvalligheids vlak. Wat belangrik is, is dat dieselfde gegroepeerde parameters gebruik kan word om ander komplekse afgeleide instrumente buite die Europese en Amerikaanse opsies te prys, dié sluit in Barrier, Asiatiese, Basket en Stuur opsies. Hierdie semi-analitiese steurings benadering is effektief vir langer termyne en onstabiel wanneer pryse naby aan die vervaldatum beraam word. As gevolg hiervan is ’n meer akkurate tegniek, die ontbinding prys benadering wat eksplisiete analitiese eerste- en tweede-orde pryse en geïmpliseerde wisselvalligheid formules gee as een van die huidige alternatiewe bespreek. Hier word slegs die metode vir Europese opsies gebruik, maar ’n uitbreiding na ander opsies kan’n idee vir verdere navorsing wees. Die enigste vereistes vir hierdie metode is integreerbaarheid en reëlmatigheid van die stogastiese wisselvalligheid proses. Korreksies tot [3] se noemenswaardige werk word ook hier bespreek.
Li, Yao. "Stochastic perturbation theory and its application to complex biological networks -- a quantification of systematic features of biological networks". Diss., Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/49013.
Pełny tekst źródłaSalhi, Rym. "Contributions to quadratic backward stochastic differential equations with jumps and applications". Thesis, Le Mans, 2019. http://www.theses.fr/2019LEMA1023.
Pełny tekst źródłaThis thesis focuses on backward stochastic differential equation with jumps and their applications. In the first chapter, we study a backward stochastic differential equation (BSDE for short) driven jointly by a Brownian motion and an integer valued random measure that may have infinite activity with compensator being possibly time inhomogeneous. In particular, we are concerned with the case where the driver has quadratic growth and unbounded terminal condition. The existence and uniqueness of the solution are proven by combining a monotone approximation technics and a forward approach. Chapter 2 is devoted to the well-posedness of generalized doubly reflected BSDEs (GDRBSDE for short) with jumps under weaker assumptions on the data. In particular, we study the existence of a solution for a one-dimensional GDRBSDE with jumps when the terminal condition is only measurable with respect to the related filtration and when the coefficient has general stochastic quadratic growth. We also show, in a suitable framework, the connection between our class of backward stochastic differential equations and risk sensitive zero-sum game. In chapter 3, we investigate a general class of fully coupled mean field forward-backward under weak monotonicity conditions without assuming any non-degeneracy assumption on the forward equation. We derive existence and uniqueness results under two different sets of conditions based on proximation schema weither on the forward or the backward equation. Later, we give an application for storage in smart grids
Schwarz, Daniel Christopher. "Price modelling and asset valuation in carbon emission and electricity markets". Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:7de118d2-a61b-4125-a615-29ff82ac7316.
Pełny tekst źródłaRoelly, Sylvie, i Myriam Fradon. "Infinite system of Brownian balls : equilibrium measures are canonical Gibbs". Universität Potsdam, 2006. http://opus.kobv.de/ubp/volltexte/2006/672/.
Pełny tekst źródłaFradon, Myriam, i Sylvie Roelly. "Infinite system of Brownian Balls: Equilibrium measures are canonical Gibbs". Universität Potsdam, 2005. http://opus.kobv.de/ubp/volltexte/2011/5159/.
Pełny tekst źródłaKleinen, Thomas Christopher. "Stochastic information in the assessment of climate change". Phd thesis, [S.l. : s.n.], 2005. http://deposit.ddb.de/cgi-bin/dokserv?idn=975745441.
Pełny tekst źródłaNoubiagain, Chomchie Fanny Larissa. "Contributions to second order reflected backward stochastic differentials equations". Thesis, Le Mans, 2017. http://www.theses.fr/2017LEMA1016/document.
Pełny tekst źródłaThis thesis deals with the second-order reflected backward stochastic differential equations (2RBSDEs) in general filtration. In the first part , we consider the reflection with a lower obstacle and then extended the result in the case of an upper obstacle . Our main contribution consists in demonstrating the existence and the uniqueness of the solution of these equations defined in the general filtration under weak assumptions. We replace the uniform regularity by the Borel regularity(through analytic measurability). The dynamic programming principle for the robust stochastic control problem is thus demonstrated under weak assumptions, that is to say without regularity on the generator, the terminal condition and the obstacle. In the standard Backward Stochastic Differential Equations (BSDEs) framework, there is a symmetry between lower and upper obstacles reflection problem. On the contrary, in the context of second order BSDEs, this symmetry is no longer satisfy because of the nonlinearity of the expectation under which our robust stochastic non-dominated stochastic control problem is defined. In the second part , we get a numerical approximation scheme of a class of second-order reflected BSDEs. In particular we show the convergence of our scheme and we test numerically the results
Celep, Saziye Betul. "Stochastic Volatility And Stochastic Interest Rate Model With Jump And Its Application On General Electric Data". Master's thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613192/index.pdf.
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