Table of Contents
ISRN Mathematical Analysis
Volume 2013, Article ID 383265, 10 pages
http://dx.doi.org/10.1155/2013/383265
Research Article

Optimization Problems of Excess-of-Loss Reinsurance and Investment under the CEV Model

1Antai College of Economics and Management, Shanghai Jiao Tong University, Shanghai 200052, China
2School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, China

Received 19 February 2013; Accepted 11 April 2013

Academic Editors: G. Gripenberg and G. Schimperna

Copyright © 2013 Qicai Li and Mengdi Gu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider that the insurer purchases excess-of-loss reinsurance and invests its wealth in the constant elasticity of variance (CEV) stock market. We model risk process by Brownian motion with drift and study the optimization problem of maximizing the exponential utility of terminal wealth under the controls of excess-of-loss reinsurance and investment. Using stochastic control theory and power transformation technique, we obtain explicit expressions for the optimal polices and value function. We also show that the optimal excess-of-loss reinsurance is always better than optimal proportional reinsurance. Some numerical examples are given.