文章基本信息

标题：Mixed Band Control of Mutual Proportional Reinsurance
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作者：Michael Taksar ; John Liu ; Jiguang Yuan 等
期刊名称：Journal of Mathematical Finance
印刷版ISSN：2162-2434
电子版ISSN：2162-2442
出版年度：2013
卷号：3
期号：2
页码：256-267
DOI：10.4236/jmf.2013.32025
出版社：Scientific Research Publishing
摘要：In this paper, we investigate the optimization of mutual proportional reinsurance—a mutual reserve system that is in- tended for the collective reinsurance needs of homogeneous mutual members, such as P&I Clubs in marine mutual in- surance and reserve banks in the US Federal Reserve, where a mutual member is both an insurer and an insured. 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 aABb, coupled with a proportional reinsurance policy (classical control), is optimal when the objective is to minimize the total maintenance cost. That is, when the reserve position reaches a lower boundary of a=0, the reserve should immedi- ately be raised to level A; when the reserve reaches an upper boundary of b, it should immediately be reduced to a level B. An interesting finding produced by the study reported in this paper is that there exists a situation such that if the up- side fixed cost is relatively large in comparison to a finite threshold, then the optimal band control is reduced to a downside only (i.e., dividend payment only) control in the form of (0, 0; B, b) with a=A=0. In this case, it is opti- mal for the mutual insurance firm to go bankrupt as soon as its reserve level reaches zero, rather than to jump restart by calling for additional contingent funds. This finding partially explains why many mutual insurance companies, that were once quite popular in the financial markets, are either disappeared or converted to non-mutual ones.
关键词：Insurance and Risk Management; Dynamic Programming and Control