Alpha-robust mean-variance reinsurance-investment strategy

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• 作者：Bin Li^a ; ^{bin.li@uwaterloo.ca" class="auth_mail" title="E-mail the corresponding author} ; Danping Li^b ; ^{lidanping@tju.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Dewen Xiong^c ; ^{xiongdewen@sjtu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：α-Maxmin utility ; Robust reinsurance-investment problem ; Mean-variance criterion ; Time-consistent equilibrium strategy ; Lé ; vy insurance model
• 刊名：Journal of Economic Dynamics and Control
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：70
• 期：Complete
• 页码：101-123
• 全文大小：699 K

文摘

Inspired by the α-maxmin expected utility, we propose a new class of mean-variance criterion, called α-maxmin mean-variance criterion, and apply it to the reinsurance-investment problem. Our model allows the insurer to have different levels of ambiguity aversion (rather than only consider the extremely ambiguity-averse attitude as in the literature). The insurer can purchase proportional reinsurance and also invest the surplus in a financial market consisting of a risk-free asset and a risky asset, whose dynamics is correlated with the insurance surplus. Closed-form equilibrium reinsurance-investment strategy is derived by solving the extended Hamilton–Jacobi–Bellman equation. Our results show that the equilibrium reinsurance strategy is always more conservative if the insurer is more ambiguity-averse. When the dependence between insurance and financial risks are weak, the equilibrium investment strategy is also more conservative if the insurer is more ambiguity-averse. However, in order to diversify the portfolio, a more ambiguity-averse insurer may adopt a more aggressive investment strategy if the insurance market is very ambiguous. For an ambiguity-neutral insurer, the investment strategy is identical to the non-robust investment strategy.