Faculty Publications

Stochastic Brownian Game Of Absolute Dominance

Document Type

Article

Keywords

Absolute dominance, Diffusion approximation, Nash equilibrium, Reinsurance, Stochastic differential game

Journal/Book/Conference Title

Journal of Applied Probability

Volume

51

Issue

2

First Page

436

Last Page

452

Abstract

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. © Applied Probability Trust 2014.

Department

Department of Mathematics

Original Publication Date

1-1-2014

DOI of published version

10.1239/jap/1402578635

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