Robust Investment and Proportional Reinsurance Strategy with Delay and Jumps in a Stochastic Stackelberg Differential Game

Qiang Zhang and Qianqian Cui ()
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Qiang Zhang: Ningxia University
Qianqian Cui: Ningxia University

Methodology and Computing in Applied Probability, 2024, vol. 26, issue 4, 1-34

Abstract: Abstract This paper discusses a robust Stackelberg differential investment and proportional reinsurance game for a reinsurance company and an insurance company, where the insurance company is treated as the follower and the reinsurance company is treated as the leader. The reinsurance company can set reinsurance premium price and invest its wealth in a savings account and a stock, where the price dynamic of the stock is governed by a jump-diffusion model. The insurance company can buy proportional reinsurance from the reinsurance company and trade in the same stock and savings account. Beside, we take historical performance into account. Both the reinsurance company and the insurance company are supposed to be ambiguity-averse and their purposes are to maximise the expected exponential utility of their final wealth with delay, respectively. By adopting stochastic control theory, we obtain the optimal value functions and robust equilibrium strategies explicitly. We also establish the corresponding verification theorem. Finally, we present numerical examples that demonstrate how the ambiguity aversion coefficients and other parameters affect the robust equilibrium strategies.

Keywords: Stackelberg differential game; Equilibrium strategy; Ambiguity; Dealy; Jump-diffusion; 91B30; 91A23; 91G10 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11009-024-10108-8

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