Optimal control of stochastic FitzHugh–Nagumo equation

Abstract

This paper is concerned with existence and uniqueness of solution for the the optimal control problem governed by the stochastic FitzHugh-Nagumo equation driven by a Gaussian noise. First order conditions of optimality are also obtained.

A BSDE with Delayed Generator Approach to Pricing under Counterparty Risk and Collateralization

“…Moreover, we underline that analogous approaches can be fruitfully exploited within frameworks characterized by stochastic optimal control problems, as has been made in, for example, [31,39]; see also the references therein.…”

H∞ boundary control for a class of nonlinear stochastic parabolic distributed parameter systems

“…Remark In analogy with some stochastic effects included in ODEs, DPSs also contain the inevitable randomness. The importance of incorporating stochastic effects in the modeling of DPSs especially for the Itô‐type systems with state‐dependent noise has been recognized in various fields such as biology, chemistry, neurophysiology, and statistical physics . What is more, many real DPSs are nonlinear.…”

A Rbsdes Approach for the Numerical Evaluation of the American Option Pricing Problem

“…Let (ξ, f, S) and (ξ ′ , f ′ , S ′ ) be two sets of data taken according to the object specifications given at points [1], [2], [3], above, but with the exception that the Lipschitz condition [2] could be satisfied by either f or f ′ only. Suppose in addition that the following inequalities hold…”

“…In fact, recursive utility corresponds to the solution of a particular BSDE associated with a generator which does not depend on z-component, see below for more details. Moreover, the BSDEs theory has been extensively used in stochastic control, see, e.g., [3] and references therein, as they appear as adjoint equations in the stochastic version of Pontryagin maximum principle, and in Mathematical Finance, since any pricing problem by replication can be written in terms of linear BSDEs, or non-linear BSDEs when portfolios constraints are taken into account, see [19,11,12,13,14].…”