Optimal investment for an insurer under liquid reserves

Haili Yuan; Yijun Hu

doi:10.3934/jimo.2019114

Article Contents

2021, Volume 17, Issue 1: 339-355. Doi: 10.3934/jimo.2019114

This issue Previous Article Robust parameter estimation for constrained time-delay systems with inexact measurements Next Article The point-wise convergence of shifted symmetric higher order power method

Optimal investment for an insurer under liquid reserves

Haili Yuan^, and
Yijun Hu

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

^* Corresponding author: Haili Yuan
^* Corresponding author: Haili Yuan

Received: December 31, 2018

Revised: February 28, 2019

Early access: September 2019

Published: January 2021

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

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Abstract

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.

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Mathematics Subject Classification: Primary: 93E20; Secondary: 60J75, 60G46.

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