Faculty Publications

A Stochastic Differential Game For Quadratic-Linear Diffusion Processes

Document Type

Article

Keywords

Fleming-Bellman-Isaacs equations, Nash equilibrium, quadratic-linear diffusion process, Stochastic differential game

Journal/Book/Conference Title

Advances in Applied Probability

Volume

48

Issue

4

First Page

1161

Last Page

1182

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.

Department

Department of Mathematics

Original Publication Date

12-1-2016

DOI of published version

10.1017/apr.2016.69

Repository

UNI ScholarWorks, Rod Library, University of Northern Iowa

Language

en

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