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Alpha-robust mean-variance reinsurance-investment strategy

Bin Li, Danping Li and Dewen Xiong

Journal of Economic Dynamics and Control, 2016, vol. 70, issue C, 101-123

Abstract: 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.

Keywords: α-Maxmin utility; Robust reinsurance-investment problem; Mean-variance criterion; Time-consistent equilibrium strategy; Lévy insurance model (search for similar items in EconPapers)
JEL-codes: C61 G11 G22 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1016/j.jedc.2016.07.001

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Journal of Economic Dynamics and Control is currently edited by J. Bullard, C. Chiarella, H. Dawid, C. H. Hommes, P. Klein and C. Otrok

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