Abstract
This paper focuses on the optimal reinsurance problem with consideration of joint interests of an insurer and a reinsurer. In our model, the risk process is assumed to follow a Brownian motion with drift. The insurer can transfer the risk to the reinsurer via proportional reinsurance, and the reinsurance premium is calculated according to the variance and standard deviation premium principles. The objective is to maximize the expected exponential utility of the weighted sum of the insurer’s and the reinsurer’s terminal wealth, where the weight can be viewed as a regularization parameter to measure the importance of each party. By applying stochastic control theory, we establish the Hamilton–Jacobi–Bellman equation and obtain explicit expressions of optimal reinsurance strategies and optimal value functions. Furthermore, we provide some numerical simulations to illustrate the effects of model parameters on the optimal reinsurance strategies.
Highlights
Since reinsurance is an effective way to spread risk in the insurance business, the problem of optimal reinsurance for insurers has drawn great attention in recent years
From equation (33), we find that the optimal reinsurance strategy is similar to those in Liang and Yuen [26], Lin and Yang [30], and Wen [31], which considered the optimal reinsurance strategies under variance premium principle only for an insurer
We consider the optimal reinsurance problem with joint interests of both an insurer and a reinsurer. e risk process is assumed to follow a Brownian motion with drift and the insurer transfers part of the risk to the reinsurer via proportional reinsurance
Summary
Since reinsurance is an effective way to spread risk in the insurance business, the problem of optimal reinsurance for insurers has drawn great attention in recent years. Li et al [23], Li et al [24], and Zhao et al [25] considered optimal reinsurance and investment problems of a general company including an insurer and a reinsurer under the expected utility maximization and mean-variance criterion, respectively. We investigate the optimal reinsurance strategies taking into account the joint interests of both an insurer and a reinsurer in a continuous-time model. (1) e explicit optimal reinsurance strategy for a dynamic model considering the joint interests of both an insurer and a reinsurer is derived.
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