Hostname: page-component-7479d7b7d-767nl Total loading time: 0 Render date: 2024-07-13T00:19:44.308Z Has data issue: false hasContentIssue false
  • English
  • Français

Locally Risk-minimizing Hedging of Insurance Payment Streams

Published online by Cambridge University Press:  17 April 2015

Martin Riesner
Martin Riesner*
Affiliation:
Abteilung für Zahlentheorie und Wahrscheinlichkeitstheorie, Fakultät für Mathematik und Wirtschaftswissenschaften Universität Ulm, Helmholtzstrasse 18, 89069 Ulm, Germany, Tel.: +497315023514, Fax: +497315023516, E-mail: martin.riesner@alumni.uni-ulm.de
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

For the martingale case Föllmer and Sondermann (1986) introduced a unique admissible risk-minimizing hedging strategy for any square-integrable contingent claim H. Schweizer (1991) developed their theory further to the semimartingale case introducing the notion of local risk-minimization. Møller (2001) extended the theory of Föllmer and Sondermann (1986) to hedge general payment processes occurring mainly in insurance. We expand local risk-minimization to the theory of hedging general payment processes and derive such a hedging strategy for general unit-linked life insurance contracts in a general Lévy process financial market.

Keywords

Local risk-minimizationsemimartingaleshedgingincomplete marketLévy processunit-linked life insuranceMarkov chain
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 37 , Issue 1 , May 2007 , pp. 67 - 91
Copyright
Copyright © ASTIN Bulletin 2007

References

Aase, K. and Persson, S.A. (1994) Pricing of unit-linked life insurance policies. Scandinavian Actuarial Journal 1, 26–52.CrossRefGoogle Scholar
Chan, T. (1999) Pricing contingent claims on stocks driven by Lévy processes. The Annals of Applied Probability 9(2), 504–528.CrossRefGoogle Scholar
Föllmer, H. and Sondermann, D. (1986) Hedging of non-redundant contingent claims. Contributions to Mathematical Economics. Hildenbrand, W., Mas-Colell, A. (eds.), North-Holland, 205–223.Google Scholar
Hoem, J. (1969) Markov chain models in life insurance. Blätter der Deutschen Gesellschaft für Versicherungsmathematik 9, 91–107.Google Scholar
Jacod, J. and Shiryaev, A.N. (2003) Limit Theorems for Stochastic Processes. 2nd ed., Springer, Berlin-Heidelberg-New York.CrossRefGoogle Scholar
Kallenberg, O. (2002) Foundations of Modern Probability. 2nd ed., Springer, New York-Berlin-Heidelberg.CrossRefGoogle Scholar
Møller, T. (1998) Risk-minimizing hedging strategies for unit-linked life insurance contracts. ASTIN Bulletin 28, 1–47.CrossRefGoogle Scholar
Møller, T. (2001) Risk-mimizing hedging strategies for insurance payment processes. Finance and Stochastics 5(4), 419–446.Google Scholar
Protter, P. (2004) Stochastic Integration and Differential Equations. 2nd ed., Springer, Berlin-Heidelberg-New York.Google Scholar
Riesner, M. (2006a) Hedging life insurance contracts in a Lévy process financial market. Insurance: Mathematics and Economics 38(3), 599–608.Google Scholar
Riesner, M. (2006b) Unit-linked life insurance in Lévy-process financial markets. Dissertation, Ulm University.Google Scholar
Schweizer, M. (1990) Risk-minimality and orthogonality of martingales. Stochastics and Stochastic Reports 30, 123–131.CrossRefGoogle Scholar
Schweizer, M. (1991) Option hedging for semimartingales. Stochastic Processes and their Applications 37, 339–363.CrossRefGoogle Scholar
Schweizer, M. (2001) A guided tour through quadratic hedging approaches. Handbooks in Mathematical Finance: Option Pricing, Interest Rates and Risk Management. Jouini, E., Cvitanic, J., Musiela, M. (eds.), Cambridge University Press, Cambridge, 538–574.Google Scholar