NDLI: Ju n 20 07 Stochastic Control Problems for Systems Driven by Normal Martingales

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Ju n 20 07 Stochastic Control Problems for Systems Driven by Normal Martingales

Content Provider	Semantic Scholar
Author	Buckdahn, Rainer Rainer, Catherine
Copyright Year	2008
Abstract	In this paper we study a class of stochastic control problems in which the control of the jump size is essential. Such a model is a generalized version for various applied problems ranging from optimal reinsurance selections for general insurance models to queueing theory. The main novel point of such a control problem is that by changing the jump size of the system, one essentially changes the type of the driving martingale. Such a feature does not seem to have been investigated in any existing stochastic control literature. We shall first provide a rigorous theoretical foundation for the control problem by establishing an existence result for the multidimensional structure equation on a Wiener-Poisson space, given an arbitrary bounded jump size control process; and by providing an auxiliary counterexample showing the non-uniqueness for such solutions. Based on these theoretical results we then formulate the control problem and prove the Bellman Principle, and derive the corresponding Hamilton-Jacobi-Bellman (HJB) equation, which in this case is a mixed second-order partial differential/difference equation. Finally we prove a uniqueness result for the viscosity solution of such an HJB equation.
File Format	PDF HTM / HTML
Alternate Webpage(s)	http://arxiv.org/pdf/0706.4018v1.pdf
Language	English
Access Restriction	Open
Subject Keyword	Bellman equation Hamilton–Jacobi–Bellman equation Jacobi method Queueing theory Recurrence relation Stochastic control Viscosity solution hamilton rating scale for depression
Content Type	Text
Resource Type	Article

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