Optimal time-consistent reinsurance and investment strategies for multiple dependent types of insurance business and a unified investment framework

This paper proposes a new insurance model, which consists of the main insurancebusiness andntypes of insurance sub-business. We consider the dependence betweenthe main insurance business and thentypes of insurance sub-business, which ismeasured by the correlation of the number of their claims. To reduce claim risk, theinsurer can simultaneously purchase reinsurance for the main insurance business andntypes of insurance sub-business, respectively. In addition, we consider a unifiedinvestment framework, which includes typical diversified and concentrated invest-ment patterns in the literature. The objective of the insurer is to find the optimal time-consistent reinsurance and investment strategies so as to maximize the expected ter-minal wealth while minimizing the variance of the terminal wealth. By using stochas-tic control theory and the Hamilton-Jacobi-Bellman equation technique, we obtainthe explicit optimal time-consistent reinsurance and investment strategies. Finally numerical examples are given to illustrate the effects of model parameters on theoptimal strategies, and analysis of the results reveals some interesting phenomena