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Stochastic Brownian Game of Absolute Dominance

Part of: Stochastic systems and control Stochastic processes

Published online by Cambridge University Press:  19 February 2016

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

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In this paper we study a reinsurance game between two insurers whose surplus processes are modeled by arithmetic Brownian motions. We assume a minimax criterion in the game. One insurer tries to maximize the probability of absolute dominance while the other tries to minimize it through reinsurance control. Here absolute dominance is defined as the event that liminf of the difference of the surplus levels tends to -∞. Under suitable parameter conditions, the game is solved with the value function and the Nash equilibrium strategy given in explicit form.

Keywords

Stochastic differential gameNash equilibriumdiffusion approximationreinsuranceabsolute dominance

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 93E20: Optimal stochastic control
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 2 , June 2014 , pp. 436 - 452
Copyright
© Applied Probability Trust 

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