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A stochastic differential game for quadratic-linear diffusion processes

Part of: Stochastic systems and control Stochastic processes

Published online by Cambridge University Press:  11 January 2017

Shangzhen Luo
Shangzhen Luo*
Affiliation:
University of Northern Iowa
*
* Postal address: Department of Mathematics, University of Northern Iowa, Cedar Falls, IA 50614-0506, USA. Email address: luos@uni.edu
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Abstract

In this paper we study a stochastic differential game between two insurers whose surplus processes are modelled by quadratic-linear diffusion processes. We consider an exit probability game. One insurer controls its risk process to minimize the probability that the surplus difference reaches a low level (indicating a disadvantaged surplus position of the insurer) before reaching a high level, while the other insurer aims to maximize the probability. We solve the game by finding the value function and the Nash equilibrium strategy in explicit forms.

Keywords

Stochastic differential gameNash equilibriumFleming–Bellman–Isaacs equationsquadratic-linear diffusion process

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 93E20: Optimal stochastic control
Type
Research Article
Information
Advances in Applied Probability , Volume 48 , Issue 4 , December 2016 , pp. 1161 - 1182
Copyright
Copyright © Applied Probability Trust 2017 

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