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2012•Stochastic Analysis and ApplicationsRequires access

Viscosity Solution of Optimal Stopping Problem for Stochastic Systems with Bounded Memory

Mou-Hsiung Chang, Tao Pang, Moustapha Pemy

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Abstract

We consider a finite time horizon optimal stopping problem for a system of stochastic functional differential equations with a bounded memory. Under some sufficiently smooth conditions, a Hamilton-Jacobi-Bellman (HJB) variational inequality for the value function is derived via dynamical programming principle. It is shown that the value function is the unique viscosity solution of the HJB variational inequality.

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What this paper is about

We consider a finite time horizon optimal stopping problem for a system of stochastic functional differential equations with a bounded memory. Under some sufficiently smooth conditions, a Hamilton-Jacobi-Bellman (HJB) variational inequality for the value function is derived via dynamical programming principle. It is shown that the value function is the unique viscosity solution of the HJB variational inequality.

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Available abstract

We consider a finite time horizon optimal stopping problem for a system of stochastic functional differential equations with a bounded memory. Under some sufficiently smooth conditions, a Hamilton-Jacobi-Bellman (HJB) variational inequality for the value function is derived via dynamical programming principle. It is shown that the value function is the unique viscosity solution of the HJB variational inequality.

Key concepts: Hamilton–Jacobi–Bellman equation, Viscosity solution, Bellman equation, Mathematics, Optimal stopping, Variational inequality, Bounded function, Applied mathematics

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