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Nested variational inequalities and related optimal starting–stopping problems

Part of: Hamilton-Jacobi theories, including dynamic programming Markov processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

M. Sun
M. Sun*
Affiliation:
The University of Alabama
*
∗ Postal address: Department of Mathematics, The University of Alabama, University, AL 35487–0350, USA.
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Abstract

This paper introduces several versions of starting-stopping problem for the diffusion model defined in terms of a stochastic differential equation. The problem could be regarded as a stochastic differential game in which the player can only decide when to start the game and when to quit the game in order to maximize his fortune. Nested variational inequalities arise in studying such a problem, with which we are able to characterize the value function and to obtain optimal strategies.

Keywords

STARTING-STOPPING GAMENESTED VARIATIONAL INEQUALITYDYNAMIC PROGRAMMING

MSC classification

Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory 60J60: Diffusion processes 49L20: Dynamic programming method 90C39: Dynamic programming
Type
Research Papers
Information
Journal of Applied Probability , Volume 29 , Issue 1 , March 1992 , pp. 104 - 115
Copyright
Copyright © Applied Probability Trust 1992 

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