Optimal time-consistent investment and reinsurance strategies for insurers under Heston鈥檚 SV model

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• 作者：Zhongfei Li^a ; ^b ; ^{lnslzf@mail.sysu.edu.cn} ; Yan Zeng^a ; ^{zengyan1984@gmail.com} ; ^{zengy36@mail.sysu.edu.cn} ; Yongzeng Lai^c ; ^ylai@wlu.ca
• 关键词：IM52 ; IE13 ; IB91
• 刊名：Insurance ; Mathematics and Economics
• 出版年：2012
• 期刊代码：25_01676687
• 类别：mt
• 出版时间：July, 2012
• 卷：51
• 期：1
• 页码：191-203
• 文件大小：802 K

摘要

This paper considers the optimal time-consistent investment and reinsurance strategies for an insurer under Heston鈥檚 stochastic volatility (SV) model. Such an SV model applied to insurers鈥?portfolio problems has not yet been discussed as far as we know. The surplus process of the insurer is approximated by a Brownian motion with drift. The financial market consists of one risk-free asset and one risky asset whose price process satisfies Heston鈥檚 SV model. Firstly, a general problem is formulated and a verification theorem is provided. Secondly, the closed-form expressions of the optimal strategies and the optimal value functions for the mean-variance problem without precommitment are derived under two cases: one is the investment-reinsurance case and the other is the investment-only case. Thirdly, economic implications and numerical sensitivity analysis are presented for our results. Finally, some interesting phenomena are found and discussed.