the stochastic reaction diffusion systems may suffer sudden shocks‎, ‎in order to explain this phenomena‎, ‎we use markovian jumps to model stochastic reaction diffusion systems‎. ‎in this paper‎, ‎we are interested in almost sure exponential stability of stochastic reaction diffusion systems with markovian jumps‎. ‎under some reasonable conditions‎, ‎we show that the trivial solution of stocha...

Reflected partial differential equations (PDEs) have important applications in financial mathematics, stochastic control, physics, and engineering. This paper aims to present a numerical method for solving high-dimensional reflected PDEs. In fact, overcoming the “dimensional curse” approximating reflection term are challenges. Some algorithms based on neural networks developed recently fail To ...

Research has shown that gang membership increases the chances of offending, antisocial behaviour and drug use. Gang membership should be acknowledged as part of crime prevention and policy designs, and when developing interventions and preventative programmes. Correctional services are designed to rehabilitate convicted offenders. We formulate a deterministic mathematical model using nonlinear ...

The aim of this set of lectures is to present the theory of backward stochastic differential equations, in short BSDEs, and its connections with viscosity solutions of systems of semi– linear second order partial differential equations of parabolic and elliptic type, in short PDEs. Linear BSDEs have appeared long time ago, both as the equations for the adjoint process in stochastic control, as ...

We provide a simple counter-example to prove and illustrate that the backward differential flow approach, proposed by Zhu, Zhao and Liu for finding a global minimizer of coercive even-degree polynomials, can converge to a local minimizer rather than a global minimizer. We provide additional counter-examples to stress that convergence to a local minimum via the backward differential flow method ...

We consider a general wealth process with a drift coefficient which is a function of the wealth process and the portfolio process with convex constraint. Existence and uniqueness of a minimal solution are established. We convert the problem of hedging American contingent claims into the problem of minimal solution of backward stochastic differential equation, and obtain the upper hedging price ...

Since Pardoux and Peng introduced backward stochastic differential equations (BSDEs in short), the theory of BSDEs has been widely developed, mainly because of a large part of problems in mathematical finance can be treated as a BSDE. However it is known that only a limited number of BSDE can be solved explicitly. To develop numerical method and numerical algorithm is very helpful, theoreticall...

In this paper, a computational technique is proposed for solving a nonlinear backward stochastic differential equation involving standard Brownian motion. The method is presented via the block pulse functions in combination with the collocation method. With using this approach, the nonlinear backward stochastic differential is reduced to a stochastic nonlinear system of 2m equations and 2m unkn...

In this paper, we consider the problem of mean-variance hedging in an incomplete market where the underlying assets are jump diffusion processes which are driven by Brownian motion and doubly stochastic Poisson processes. This problem is formulated as a stochastic control problem and closed form expressions for the optimal hedging policy are obtained using methods from stochastic control and th...