Stochastic optimization problems arise in decision-making problems under uncertainty, and find various applications in economics and finance. On the other hand, problems in finance have recently led to new developments in the theory of stochastic control. This volume provides a systematic treatment of stochastic optimization problems applied to finance by presenting the different existing methods: dynamic programming, viscosity solutions, backward stochastic differential equations, and martingale duality methods. The theory is discussed in the context of recent developments in this field, with complete and detailed proofs, and is illustrated by means of concrete examples from the world of finance: portfolio allocation, option hedging, real options, optimal investment, etc. This book is directed towards graduate students and researchers in mathematical finance, and will also benefit applied mathematicians interested in financial applications and practitioners wishing to know more about the use of stochastic optimization methods in finance.

Continuous-time stochastic control and optimization with financial applications / Huyen Pham

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Stochastic Differential Equations And Applications

Stochastic Population Models in Ecology and Epidemiology

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Numerical Solution Of Sde Through Computer Experiments

Extinction and stationary distribution of a stochastic COVID-19 epidemic model with time-delay

In this paper, we establish the existence of a unique global positive solution for a stochastic epidemic model, incorporating media coverage and driven by Levy noise. We also investigate the dynamic properties of the solution around both disease-free and endemic equilibria points of the deterministic model. Furthermore, we present some numerical results to support the theoretical work.

A stochastic SIRS epidemic model incorporating media coverage and driven by Lévy noise

Stochastic stability and instability of an epidemic model with relapse

In this work, we investigate a stochastic epidemic model with relapse and distributed delay. First, we prove that our model possesses and unique global positive solution. Next, by means of the Lyapunov method, we determine some sufficient criteria for the extinction of the disease and its persistence. In addition, we establish the existence of a unique stationary distribution to our model. Finally, we provide some numerical simulations for the stochastic model to assist and show the applicability and efficiency of our results.

Analysis of a stochastic distributed delay epidemic model with relapse and Gamma distribution kernel

Some diseases such as herpes, bovine and human tuberculosis exhibit relapse in which the recovered individuals do not acquit permanent immunity but return to infectious class Such diseases are modeled by SIRI models In this paper, we establish the existence of a unique global positive solution for a stochastic epidemic model with relapse and jumps We also investigate the dynamic properties of the solution around both disease-free and endemic equilibria points of the deterministic model Furthermore, we present some numerical results to support the theoretical work

https://www.aimsciences.org/article/exportPdf?id=dc4b65ce-1afb-4def-846f-c604d2fb6d1f

A stochastic SIRI epidemic model with Lévy noise

In this paper, we analyze a stochastic coronavirus (COVID-19) epidemic model which is perturbed by both white noise and telegraph noise incorporating general incidence rate. Firstly, we investigate the existence and uniqueness of a global positive solution. Then, we establish the stochastic threshold for the extinction and the persistence of the disease. The data from Indian states, are used to confirm the results established along this paper.

/pdf/dynamics-of-a-stochastic-coronavirus-covid-19-epidemic-model-1mo8adjujp.pdf

Mohamed El Fatini

Papers

A stochastic SIRS epidemic model incorporating media coverage and driven by Lévy noise

Stochastic stability and instability of an epidemic model with relapse

Analysis of a stochastic distributed delay epidemic model with relapse and Gamma distribution kernel

A stochastic SIRI epidemic model with Lévy noise

Dynamics of a stochastic coronavirus (COVID-19) epidemic model with Markovian switching.