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Optimal non-proportional reinsurance control and stochastic differential games

Michael Taksar
(University of Missouri)
Thiele Seminar
Thursday, 2 September, 2010, at 13:15-14:00, in Koll. D (1531-211)
We study a competition between two companies in the framework of the insurance market. Each of the companies has a goal to take over the other one. It is assumed that when the difference of the surpluses becomes large enough than the company with the largest surplus takes over its competitor. The companies can reduce their business risk by applying reinsurance (which also reduces their potential profit). The objective of each company is to maximize probability to take over the other company. We formulate this problem as a stochastic differential game and describe its Nash equilibrium. A closed form solution for this game is found. It is shown that finding the Nash equilibrium is equivalent to finding saddle points for a family of functions of two variables.
Organised by: The T.N. Thiele Centre
Contact person: Steen Thorbjørnsen