# American Institute of Mathematical Sciences

January  2021, 17(1): 339-355. doi: 10.3934/jimo.2019114

## Optimal investment for an insurer under liquid reserves

 School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei 430072, China

* Corresponding author: Haili Yuan

Received  January 2019 Revised  March 2019 Published  January 2021 Early access  September 2019

Fund Project: Supported by National Natural Science Foundation of China (Nos. 11201352, 11771343)

In this paper, we study the optimal investment problem for an insurer, who is allowed to invest in a financial market which consists of $N$ risky securities modeled by an $N$-dimensional Itô process. The surplus of the insurer is modeled by a general risk model. For the insurer's wealth, some money (called liquid reserves) can only be used to cope with risk, and can not be invested in the financial market. We suggest that the liquid reserve is a proportion of the total claim amount. By the martingale approach, we derive the optimal strategies for the CARA and the quadratic utilities, respectively.

Citation: Haili Yuan, Yijun Hu. Optimal investment for an insurer under liquid reserves. Journal of Industrial & Management Optimization, 2021, 17 (1) : 339-355. doi: 10.3934/jimo.2019114
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