The optimal investment and re-guarantee purchase of China's financing guarantee institutions considering risk preference

Financing guarantee institutions achieve capital preservation and appreciation through investment, and diversify business risks by purchasing re-guarantee. In order to study the optimal investment and re-guarantee purchase strategies of financing guarantee institutions, the geometric Brownian motion modulated by Markov chain modulation is selected to describe the price process of risk assets, the Hamilton-Jacobi-Bellman equation is constructed based on the utility maximization criterion, and the solutions of optimal investment and re-guarantee purchase strategies are discussed under the exponential utility function. Ultimately, the influence of relevant parameter on optimal strategies is studied by computational experimental simulation method. The results showed that the risk-free interest rate, risk aversion coefficient and guarantee period have significant effects on the optimal investment and re-guarantee purchase strategies. The market mechanism only affects the trend of the optimal investment strategy, but has no effect on the optimal re-guarantee purchase strategy. However, the increase of the re-guarantee institution's safety loading and the guarantee recovery rate will significantly reduce the re-guarantee purchase ratio.