Locally risk-minimizing hedging strategies for unit-linked life insurance contracts under a regime switching Lévy model

Abstract

This paper extends the model and analysis in that of Vandaele and Vanmaele [Insurance: Mathematics and Economics, 2008, 42: 1128–1137]. We assume that parameters of the Lévy process which models the dynamic of risky asset in the financial market depend on a finite state Markov chain. The state of the Markov chain can be interpreted as the state of the economy. Under the regime switching Lévy model, we obtain the locally risk-minimizing hedging strategies for some unit-linked life insurance products, including both the pure endowment policy and the term insurance contract.

Keywords

Unit-linked life insurance / Lévy process / regime switching / risk-minimization

References

[1.] Chan T. Pricing contingent claims on stocks driven by Lévy processes. The Annals of Applied Probability, 1999, 9 2 504-528

[2.] Deshpande A., Ghosh M. K. Risk minimizing option pricing in a regime switching market. Stochastic Analysis and Applications, 2008, 26, 313-324

[3.] Föllmer H., Schweizer M. Davis M., Elliot R. Hedging of contingent claims under incomplete information. Applied Stochastic Analysis. Stochastic Monographs, Vol 5, 1991, New York: Gordon and Breach 389-414

[4.] Föllmer H., Sondermann D. Hildenbrand W., Mas-Colell A. Hedging of non-redundant contingent claims. Contributions to Mathematical Economics, 1986, Amsterdam: North-Holland 205-223

[5.] Ghosh M. K., Arapostathis A., Marcus S. I. Ergodic control of switching diffusions. SIAM Journal of Contral and Optimization, 1997, 35, 1952-1988

[6.] Møller T. Risk-minimizing hedging strategies for unit-linked life insurance contracts. ASTIN Bulletin, 1998, 28, 17-47

[7.] Møller T. Risk-minimizing hedging strategies for insurance payment processes. Finance and Stochastics, 2001, 5 4 419-446

[8.] Riesner M. Hedging life insurance contracts in a Lévy process financial market. Insurance: Mathematics and Economics, 2006, 38, 599-608

[9.] Schweizer M. Option hedging for semimartingales. Stochastic Processes and Their Applications, 1991, 37, 339-363

[10.] Schweizer M. Risk-minimizing hedging strategies under restricted information. Mathematical Finance, 1994, 4, 327-342

[11.] Schweizer M. Jouini E., Cvitanić J., Musiela M. A guided tour through quadratic hedging approaches. Handbooks in Mathematical Finance: Option Pricing, Interest Rates and Risk Management, 2001, Cambridge: Cambridge University Press 538-574

[12.] Vandaele N., Vanmaele M. A locally risk-minimizing hedging strategy for unit-linked life insurance contracts in a Lévy process financial market. Insurance: Mathematics and Economics, 2008, 42, 1128-1137