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Robust equilibrium excess-of-loss reinsurance and CDS investment strategies for a mean–variance insurer with ambiguity aversion

Hui Zhao, Yang Shen, Yan Zeng and Wenjun Zhang

Insurance: Mathematics and Economics, 2019, vol. 88, issue C, 159-180

Abstract: This paper considers the robust equilibrium reinsurance and investment strategies for an ambiguity-averse insurer under a dynamic mean–variance criterion. The insurer is allowed to purchase excess-of-loss reinsurance and invest in a financial market consisting of a risk-free asset and a credit default swap (CDS). Following a game theoretic approach, robust equilibrium strategies and equilibrium value functions for the pre-default case and the post-default case are derived, respectively. For the ambiguity-averse insurer, in general the equilibrium strategies can be characterized by unique solutions to some algebraic equations. For the degenerate case with an ambiguity-neutral insurer, closed-form expressions of equilibrium strategies and equilibrium value functions are obtained. Numerical examples demonstrate that the consideration of model uncertainty and CDS investment improves the insurer’s utility. In this regard, our paper establishes theoretical and numerical support for the importance of ambiguity aversion, credit risk and their interplay in insurance business.

Keywords: Excess-of-loss reinsurance; Credit default swap; Mean–variance criterion; Model uncertainty; Robust equilibrium strategy (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.insmatheco.2019.06.007

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