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

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.

Keywords:

• Ambiguity-averse
• constant elasticity of variance
• default risk
• investment
• reinsurance

Notes

1 Please refer to https://www.naic.org/capital.marketsarchive/180816.pdf for capital market special report: bond breakdown by sector and insurer type.

Additional information

Funding

This work is supported by a grant from the National Natural Science Foundation of China (grant Nos. 71701068, 11701175, 11671132), the Natural Science Foundation of Hunan Province, China (No. 2018JJ3360), and the Scientific Research Fund of Hunan Provincial Education Department, China (Nos. 19B343, 17C1001, 17K057).