Journal of Probability and Statistics
Volume 2011 (2011), Article ID 850727, 23 pages
Research Article

Optimal Hedging and Pricing of Equity-Linked Life Insurance Contracts in a Discrete-Time Incomplete Market

Department of Mathematical Sciences, Bentley University, 175 Forest Street, Waltham, MA 02452-4705, USA

Received 26 May 2011; Accepted 1 September 2011

Academic Editor: Tomasz J. Kozubowski

Copyright © 2011 Norman Josephy et al. 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.


We present a method of optimal hedging and pricing of equity-linked life insurance products in an incomplete discrete-time financial market. A pure endowment life insurance contract with guarantee is used as an example. The financial market incompleteness is caused by the assumption that the underlying risky asset price ratios are distributed in a compact interval, generalizing the assumptions of multinomial incomplete market models. For a range of initial hedging capitals for the embedded financial option, we numerically solve an optimal hedging problem and determine a risk-return profile of each optimal non-self-financing hedging strategy. The fair price of the insurance contract is determined according to the insurer's risk-return preferences. Illustrative numerical results of testing our algorithm on hypothetical insurance contracts are documented. A discussion and a test of a hedging strategy recalibration technique for long-term contracts are presented.