Robust optimal strategies for an insurer under generalized mean-variance premium principle with defaultable bond

Yingchun Deng, Man Li, Ya Huang and Jieming Zhou

Communications in Statistics - Theory and Methods, 2020, vol. 50, issue 21, 5126-5159

Abstract: In this paper, we analyze a robust optimal investment-reinsurance problem involving a defaultable security for an ambiguity-averse insurer(AAI), who worries about uncertainty in model parameters. The insurer can trade in a risk-free asset, a stock and a defaultable corporate bond. The price process of the stock is described by a constant elasticity of variance(CEV) model. In particular, the reinsurance premium is calculated according to the generalized mean-variance premium principle. Using the dynamic programing approach, we study the pre-default case and the post-default case respectively, and then derive the optimal strategies and the corresponding value functions under the worst-case scenario. Moreover, the verification theorem is given under an inequality condition. Finally, we give some numerical examples to illustrate our main results.

Date: 2020
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DOI: 10.1080/03610926.2020.1726391

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