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In this paper we investigate the optimal control problem for a class of stochastic Cauchy evolution problem with non standard boundary dynamic and control. The model is composed by an infinite dimensional dynamical system coupled with a finite dimensional dynamics, which describes the boundary conditions of the internal system. In other terms, we are concerned with non standard boundary conditions, as the value at the boundary is governed by a different stochastic differential equation.
This paper shows that penalized backward stochastic differential equation (BSDE), which is often used to approximate and solve the corresponding reflected BSDE, admits both optimal stopping representation and optimal control representation. The new f
We study the problem of optimal inside control of an SPDE (a stochastic evolution equation) driven by a Brownian motion and a Poisson random measure. Our optimal control problem is new in two ways: (i) The controller has access to inside information,
We consider a general class of high order weak approximation schemes for stochastic differential equations driven by Levy processes with infinite activity. These schemes combine a compound Poisson approximation for the jump part of the Levy process w
In this paper we study the optimal stochastic control problem for stochastic differential systems reflected in a domain. The cost functional is a recursive one, which is defined via generalized backward stochastic differential equations developed by
We identify the stochastic processes associated with one-sided fractional partial differential equations on a bounded domain with various boundary conditions. This is essential for modelling using spatial fractional derivatives. We show well-posednes