Robust Dividend, Financing, and Reinsurance Strategies Under Model Uncertainty with Proportional Transaction Costs

Abstract

This article studies the robust dividend, financing, and reinsurance strategies for an ambiguity aversion insurer (AAI) under model uncertainty. The AAI controls its liquid reserves by purchasing proportional reinsurance, paying dividends, and issuing new equity. We consider model uncertainty and suppose that the AAI is ambiguous about the liquid reserves process, which is described by a class of equivalent probability measures. The objective of the AAI is to maximize the expected present value of the dividend payouts minus the discounted costs of issuing new equity before bankruptcy under the worst-case scenario. A detailed proof of the verification theorem is shown for the robust singular-regular problem. We obtain the explicit solutions of the robust strategies, which are classified into three cases. Numerical results are also presented to show the impacts of the ambiguity aversion coefficient, and the transaction cost factor.

ACKNOWLEDGMENTS

The authors are grateful to the members of the group of Actuarial Science and Mathematical Finance in the Department of Mathematical Sciences, Tsinghua University for their feedback and useful conversations.

Notes

1 Chakraborty, Cohen, and Young (2021) proved the uniqueness of the solution in the optimal dividends problem under model uncertainty. The penalty term in Chakraborty, Cohen, and Young (2021) does not contain the value function, and the explicit solution is not derived. In our work, to obtain an explicit solution, we add the value function in the penalty term and the uniqueness is not proved. As such, we call the dividend barrier the smooth-pasting boundary instead.

Additional information

Funding

The authors acknowledge support from the National Natural Science Foundation of China (Grant Nos. 11901574, 12271290, 11871036), the MOE Project of Key Research Institute of Humanities and Social Sciences (22JJD910003), and the National Social Science Fund of China (20AZD075). YL gratefully acknowledges financial support from the research startup fund at The Chinese University of Hong Kong, Shenzhen.