Abstract

http://ssrn.com/abstract=1316223
 
 

References (31)



 
 

Citations (1)



 


 



An Insurance Risk Model with Stochastic Volatility


Yichun Chi


China Institute for Actuarial Science, Central University of Finance and Economics

Sebastian Jaimungal


University of Toronto - Department of Statistics

X. Sheldon Lin


University of Toronto

December 15, 2008

Insurance: Mathematics and Economics, Vol. 46, No. 1, pp. 52-66

Abstract:     
In this paper, we extend the Cramer-Lundberg insurance risk model perturbed by diffusion to incorporate stochastic volatility and study the resulting Gerber-Shiu expected discounted penalty (EDP) function. Under the assumption that volatility is driven by an underlying Ornstein-Uhlenbeck (OU) process, we derive the integro-differential equation which the EDP function satisfies. Not surprisingly, no closed-form solution exists; however, assuming the driving OU process is fast mean-reverting, we apply singular perturbation theory to obtain an asymptotic expansion of the solution. Two integro-differential equations for the first two terms in this expansion are obtained and explicitly solved. When the claim size distribution is of phase-type, the asymptotic results simplify even further and we succeed in estimating the error of the approximation. Hyper-exponential and mixed-Erlang distributed claims are considered in some detail.

Number of Pages in PDF File: 31

Keywords: Gerber-Shiu expected discounted penalty function, Integro-differential equation, Singular perturbation theory, Stochastic volatility, Perturbed compound Poisson risk process, Phase-type distribution, Ornstein-Uhlenbeck process

Accepted Paper Series


Download This Paper

Date posted: December 15, 2008 ; Last revised: February 16, 2010

Suggested Citation

Chi, Yichun and Jaimungal, Sebastian and Lin, X. Sheldon, An Insurance Risk Model with Stochastic Volatility (December 15, 2008). Insurance: Mathematics and Economics, Vol. 46, No. 1, pp. 52-66. Available at SSRN: http://ssrn.com/abstract=1316223

Contact Information

Yichun Chi
China Institute for Actuarial Science, Central University of Finance and Economics ( email )
Beijing, 100081
China
Sebastian Jaimungal (Contact Author)
University of Toronto - Department of Statistics ( email )
100 St. George St.
Toronto, Ontario M5S 3G3
Canada
HOME PAGE: http://www.utstat.utoronto.ca/sjaimung
Xiaodong Sheldon Lin
University of Toronto ( email )
Department of Statistical Sciences
100 St George Street
Toronto, Ontario M5S 3G3
Canada
Feedback to SSRN


Paper statistics
Abstract Views: 1,611
Downloads: 360
Download Rank: 46,049
References:  31
Citations:  1

© 2014 Social Science Electronic Publishing, Inc. All Rights Reserved.  FAQ   Terms of Use   Privacy Policy   Copyright   Contact Us
This page was processed by apollo8 in 0.266 seconds