Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-27T07:33:19.701Z Has data issue: false hasContentIssue false
  • English
  • Français

A Stochastic Differential Game with Safe and Risky Choices

Published online by Cambridge University Press:  27 July 2009

J. M. McNamara
J. M. McNamara
Affiliation:
School ofMathematics University of Bristol Bristol, BS8 1TW England
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper considers a two-person zero-sum stochastic differential game. The dynamics of the game are given by a one-dimensional stochastic differential equation whose diffusion coefficient may be controlled by the players. The drift coefficient is held constant and cannot be controlled. Player l's objective is to maximize the probability that the state at final time, T, is positive, while Player 2's objective is to maximize the probability that the state is negative.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 2 , Issue 1 , January 1988 , pp. 31 - 39
Copyright
Copyright © Cambridge University Press 1988

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Elliot, R.J. (1976). The existence of value in stochastic differential games, SIAM Journal of Control 14: 85–94.CrossRefGoogle Scholar
Elliot, R.J. (1977). The existence of optimal strategies and saddle points in stochastic differential games. In Differential games and applications. In Hagedorn, P. (ed.), Lecture Notes in Control and Information Science. Berlin: Springer-Verlag.Google Scholar
Elliot, R.J. & Davis, M.H.A. (1981). Optimal play in a stochastic differential game. SIAM Journal of Control 19: 543–554.CrossRefGoogle Scholar
Fleming, W.H. & Rishel, R.W. (1975). Deterministic and stochastic optimal control. Berlin:Springer-Verlag.CrossRefGoogle Scholar
McNamara, J.M. (1982). Sequential choice between high-risk and safe alternatives. University of Bristol School of Mathematics Internal Report S-82−04.Google Scholar
McNamara, J.M. (1984). Control of a diffusion by switching between two drift-diffusion coefficient pairs. SIAM Journal of Control 22: 87–94.CrossRefGoogle Scholar
McNamara, J.M. (1983). Optimal control of the diffusion coefficient of a simple diffusion process. Mathematical Operations Research 8: 373–381.CrossRefGoogle Scholar
Nakao, S. (1972). On pathwise uniqueness of solutions of one-dimensional stochastic differential equations. Osaka Journal of Mathematics 9: 513–518.Google Scholar