## Abstract and Applied Analysis

### Optimal Investment for Insurers with the Extended CIR Interest Rate Model

#### Abstract

A fundamental challenge for insurance companies (insurers) is to strike the best balance between optimal investment and risk management of paying insurance liabilities, especially in a low interest rate environment. The stochastic interest rate becomes a critical factor in this asset-liability management (ALM) problem. This paper derives the closed-form solution to the optimal investment problem for an insurer subject to the insurance liability of compound Poisson process and the stochastic interest rate following the extended CIR model. Therefore, the insurer’s wealth follows a jump-diffusion model with stochastic interest rate when she invests in stocks and bonds. Our problem involves maximizing the expected constant relative risk averse (CRRA) utility function subject to stochastic interest rate and Poisson shocks. After solving the stochastic optimal control problem with the HJB framework, we offer a verification theorem by proving the uniform integrability of a tight upper bound for the objective function.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 129474, 12 pages.

Dates
First available in Project Euclid: 2 October 2014

https://projecteuclid.org/euclid.aaa/1412278812

Digital Object Identifier
doi:10.1155/2014/129474

Mathematical Reviews number (MathSciNet)
MR3230506

Zentralblatt MATH identifier
07021766

#### Citation

Chiu, Mei Choi; Wong, Hoi Ying. Optimal Investment for Insurers with the Extended CIR Interest Rate Model. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 129474, 12 pages. doi:10.1155/2014/129474. https://projecteuclid.org/euclid.aaa/1412278812

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