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Optimal investment and reinsurance of an insurer with model uncertainty

Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.14/138029

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Title: Optimal investment and reinsurance of an insurer with model uncertainty
Related: Insurance, mathematics and economics, Vol. 45, No. 1, (2009), p.81-88
DOI: 10.1016/j.insmatheco.2009.04.001
Publisher: Elsevier BV
Date: 2009
FoR/RFCD Code(s): 010400 Statistics 140200 Applied Economics
Author/Creator: Zhang, Xin
Author/Creator: Siu, Tak Kuen
Description: We introduce a novel approach to optimal investment–reinsurance problems of an insurance company facing model uncertainty via a game theoretic approach. The insurance company invests in a capital market index whose dynamics follow a geometric Brownian motion. The risk process of the company is governed by either a compound Poisson process or its diffusion approximation. The company can also transfer a certain proportion of the insurance risk to a reinsurance company by purchasing reinsurance. The optimal investment–reinsurance problems with model uncertainty are formulated as two-player, zero-sum, stochastic differential games between the insurance company and the market. We provide verification theorems for the Hamilton–Jacobi–Bellman–Isaacs (HJBI) solutions to the optimal investment–reinsurance problems and derive closed-form solutions to the problems.
Description: 8 page(s)
Subject Keyword: 010400 Statistics
Subject Keyword: 140200 Applied Economics
Subject Keyword: Optimal investment
Subject Keyword: Proportional reinsurance
Subject Keyword: Model uncertainty
Subject Keyword: Stochastic differential game
Subject Keyword: Exponential utility
Subject Keyword: Penalty of ruin
Subject Keyword: HJBI equations
Resource Type: journal article
Organisation: Macquarie University. Dept. of Actuarial Studies

Identifier: http://hdl.handle.net/1959.14/138029
Identifier: ISSN:0167-6687
Identifier: mq-rm-2009002175
Language: eng
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