Band Control of Mutual Proportional Reinsurance

Details Band Control of Mutual Proportional Reinsurance Band Control of Mutual Proportional Reinsurance

2011-12-19

arxiv.org/abs/1112.4458v1

Mathematics

Optimization and Control

Scientific paper

In this paper, we investigate the optimization of mutual proportional reinsurance --- a mutual reserve system that is intended for the collective reinsurance needs of homogeneous mutual members, such as P&I Clubs in marine mutual insurance and reserve banks in the U.S. Federal Reserve. Compared to general (non-mutual) insurance models, which involve one-sided impulse control (i.e., either downside or upside impulse) of the underlying insurance reserve process that is required to be positive, a mutual insurance differs in allowing two-sided impulse control (i.e., both downside and upside impulse), coupled with the classical proportional control of reinsurance. We prove that a special band-type impulse control $(a,A,B,b)$ with $a=0$ and $a

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