JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (11): 1-14,26.doi: 10.6040/j.issn.1671-9352.0.2022.265

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Optimal reinsurance contract design based on Stackelberg game

Peng YANG1(),Xiaoyan ZHANG2   

  1. 1. School of Mathematics, Xi'an University of Finance and Economics, Xi'an 710100, Shaanxi, China
    2. Xi'an Changfeng Research Institute of Mechanism and Electricity, Xi'an 710065, Shaanxi, China
  • Received:2022-04-29 Online:2023-11-20 Published:2023-11-07

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Abstract:

For the optimal reinsurance contract design problem, that is, the reinsurance premium pricing problem, we assume that there is an insurance company and a reinsurance company on the market. Among them, the insurance company is engaged in two types of insurance business, and the reinsurance company is engaged in one type of insurance business. To reflect the competition between the insurance company and the reinsurance company, we assume that these three insurance businesses are interdependent, and the insurance company can engage in the reinsurance business. Using the relative performance, the competition between the insurance company and the reinsurance company is quantified. The aims of the insurance company and the reinsurance company are to find an optimal reinsurance contract to maximize the mean of the terminal wealth and minimize the variance of the terminal wealth. Under the Stackelberg game framework, by using stochastic calculus and stochastic control theory, the explicit solutions for the optimal reinsurance contract and the optimal value function are obtained. Finally, the influence of model parameters on the optimal reinsurance contract is analyzed through numerical experiments and the relationship between some special cases and general cases is compared.

Key words: reinsurance contract, reinsurance premium, insurance business dependence, relative performance, Stackelberg game

CLC Number: 

  • O211.6

Fig.1

Effects of whether the reinsurance company is engaged in insurance business and τ1 on the optimal reinsurance contract"

Fig.2

Effects of whether the reinsurance company is engaged in insurance business and τ2 on the optimal reinsurance contract"

Fig.3

Effects of whether the reinsurance company is engaged in insurance business and λ on the optimal reinsurance contract"

Fig.4

Effects of whether the dependence between insurance businesses is considered and λ on the optimal reinsurance contract"

Fig.5

Effects of whether the insurance company is considered competition and λ on the optimal reinsurance contract"

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