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On Valuation and Risk Management at the Interface of Insurance and Finance

Published online by Cambridge University Press:  10 June 2011

T. Møller Ph.D.
T. Møller Ph.D.
Affiliation:
Laboratory of Actuarial Mathematics, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark., Tel: +45 35 32 07 94, Fax: +45 35 32 07 72, Email: [email protected]
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Abstract

This paper reviews methods for hedging and valuation of insurance claims with an inherent financial risk, with special emphasis on quadratic hedging approaches and indifference pricing principles and their applications in insurance. It thus addresses aspects of the interplay between finance and insurance, an area which has gained considerable attention during the past years, in practice as well as in theory. Products combining insurance risk and financial risk have gained considerable market shares. Special attention is paid to unit-linked life insurance contracts, and it is demonstrated how these contracts can be valued and hedged by using traditional methods as well as more recent methods from incomplete financial markets such as risk-minimisation, mean-variance hedging, super-replication and indifference pricing with mean-variance utility functions.

Keywords

Actuarial Valuation PrinciplesFinancial RiskHedgingIncomplete MarketIndifference PricingUnit-Linked ContractsFinancial Stop-Loss Contracts
Type
Sessional meetings: papers and abstracts of discussions
Information
British Actuarial Journal , Volume 8 , Issue 4 , 01 October 2002 , pp. 787 - 827
Copyright
Copyright © Institute and Faculty of Actuaries 2002

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References

Aase, K.K. (1993). Premiums in a dynamic model of a reinsurance market. Scandinavian Actuarial Journal, 134–160.Google Scholar
Aase, K.K. & Persson, S.A. (1994). Pricing of unit-linked life insurance policies. Scandinavian Actuarial Journal, 26–52.CrossRefGoogle Scholar
Bachelier, L. (1900). Theorie de la speculation. Annales Scientifiques de l'Ecole Normale Superieure, 17, 21–86.CrossRefGoogle Scholar
Bacinello, A.R. & Ortu, F. (1993a). Pricing equity-linked life insurance with endogenous minimum guarantees. Insurance: Mathematics and Economics, 12, 245–257.Google Scholar
Bacinello, A.R. & Ortu, F. (1993b). Pricing guaranteed securities-linked life insurance under interest-rate risk. Proceedings of the 3rd AFIR Colloquium, Rome, I, 35–55.Google Scholar
Bacinello, A.R. & Persson, S.A. (1998). Design and pricing of equity-linked life insurance under stochastic interest rates. Preprint, Institute of Finance and Management Science, The Norwegian School of Economics and Business Administration.Google Scholar
Black, F. & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637–654.CrossRefGoogle Scholar
Bouleau, N. & Lamberton, D. (1989). Residual risks and hedging strategies in Markovian markets. Stochastic Processes and their Applications, 33, 131–150.CrossRefGoogle Scholar
Braun, H. (1937). Urkunden und materialien zur geschichte der lebensversicherung und der lebensversicherungstechnik. Veröffentlichungen des Deutschen Vereins für VersicherungsWissenschaft, Heft 58, Verlag von E.S. Mittler & Sohn, Berlin.Google Scholar
Brennan, M.J. & Schwartz, E.S. (1979a). Alternative investment strategies for the issuers of equity-linked life insurance with an asset value guarantee. Journal of Business, 52, 63–93.CrossRefGoogle Scholar
Brennan, M.J. & Schwartz, E.S. (1979b). Pricing and investment strategies for guaranteed equity-linked life insurance. Monograph no. 7/The S. S. Huebner Foundation for Insurance Education, Wharton School, University of Pennsylvania, Philadelphia.Google Scholar
Bühlmann, H. (1970). Mathematical methods in risk theory, Springer-Verlag, Berlin.Google Scholar
Bühlmann, H. (1980). An economic premium principle. ASTIN Bulletin, 11, 52–60.CrossRefGoogle Scholar
Bühlmann, H. (1984). The general economic premium principle. ASTIN Bulletin, 14, 13–21.CrossRefGoogle Scholar
Bühlmann, H., Delbaen, F., Embrechts, P. & Shiryaev, A. (1997). No-arbitrage, change of measure and conditional Esscher transforms. CWI Quaterly, Amsterdam, 9(4), 291–317.Google Scholar
Cox, J., Ross, S. & Rubinstein, M. (1979). Option pricing: a simplified approach. Journal of Financial Economics, 7, 229–263.CrossRefGoogle Scholar
Cox, S.H. & Pedersen, H.W. (2000). Catastrophe risk bonds. North American Actuarial Journal, 4(4), 56–82.CrossRefGoogle Scholar
Cummins, J.D. & Geman, H. (1995). Pricing catastrophe insurance futures and call spreads: an arbitrage approach. Journal of Fixed Income, 4, 46–57.CrossRefGoogle Scholar
Cvitanić, J. (2000). Minimizing expected loss of hedging in incomplete and constrained markets. SIAM Journal on Control and Optimization, 38, 1050–1066.CrossRefGoogle Scholar
Dana, R.A. (1999). Existence, uniqueness and determinacy of equilibrium in C.A.P.M. with a riskless asset. Journal of Mathematical Economics, 32, 167–175.CrossRefGoogle Scholar
Davis, M.H.A. (1997). Option pricing in incomplete markets. In Dempster, M.A.H. & Pliska, S.R. (eds), Mathematics of derivative securities. Cambridge University Press, 216–226.Google Scholar
de Waegenaere, A. & Delbaen, F. (1992). A dynamic reinsurance theory. Insurance: Mathematics and Economics, 14, 205–218.Google Scholar
Delbaen, F. (1986). Equity linked policies. Bulletin de l'Association Royale des Actuaires Belges. 33–52.Google Scholar
Delbaen, F. & Haezendonck, J. (1989). A martingale approach to premium calculation principles in an arbitrage free market. Insurance: Mathematics and Economics, 8, 269–277.Google Scholar
Duffie, D. (1996). Dynamic asset pricing theory, 2nd ed.Princeton University Press, Princeton, New Jersey.Google Scholar
Duffie, D. & Richardson, H.R. (1991). Mean-variance hedging in continuous time. Annals of Applied Probability, 1, 1–15.CrossRefGoogle Scholar
El Karoui, N. & Quenez, M.C. (1995). Dynamic programming and pricing of contingent claims in an incomplete market. SIAM Journal on Control and Optimization, 33, 29–66.CrossRefGoogle Scholar
Embrechts, P. (2000). Actuarial versus financial pricing of insurance. Journal of Risk Finance, 1(4), 17–26.CrossRefGoogle Scholar
Föllmer, H. & Leukert, P. (1999). Quantile hedging. Finance and Stochastics, 3, 251–273.CrossRefGoogle Scholar
Föllmer, H. & Leukert, P. (2000). Efficient hedging: cost versus shortfall risk. Finance and Stochastics, 4, 117–146.Google Scholar
Föllmer, H. & Sondermann, D. (1986). Hedging of non-redundant contingent claims. In Hildenbrand, W. & Mas-Colell, A. (eds), Contributions to mathematical economics, North-Holland, 205–223.Google Scholar
Gerber, H.U. (1979). An introduction to mathematical risk theory. Monograph no. 8/The S. S. Huebner Foundation for Insurance Education, Wharton School, University of Pennsylvania, Philadelphia.Google Scholar
Gerber, H.U. (1986). Lebensversicherungsmathematik. Springer-Verlag, Berlin.CrossRefGoogle Scholar
Gerber, H.U. & Pafumi, G. (1998). Utility functions: from risk theory to finance. North American Actuarial Journal, 2(3), 74–91.CrossRefGoogle Scholar
Gerber, H.U. & Shiu, E.S.W. (1996). Actuarial bridges to dynamic hedging and option pricing. Insurance: Mathematics and Economics, 18, 183–218.Google Scholar
Gisler, A. & Frost, P. (1999). An addendum and a short comment on the paper: ‘Estimating the value of the WinCAT coupons of the Winterthur Insurance convertible bond: a study of the model risk’. ASTIN Bulletin, 29, 165–171.CrossRefGoogle Scholar
Goovaerts, M.J., De Vylder, F. & Haezendonck, J. (1984). Insurance premiums: theory and applications. North-Holland.Google Scholar
Harrison, J.M. & Kreps, D.M. (1979). Martingales and arbitrage in multiperiod securities markets. Journal of Economic Theory, 20, 381–408.CrossRefGoogle Scholar
Harrison, J.M. & Pliska, S.R. (1981). Martingales and stochastic integrals in the theory of continuous trading. Stochastic Processes and their Applications, 11, 215–260.CrossRefGoogle Scholar
Heilmann, W.R. (1987). Grundbegriffe der risikotheorie. Verlag Versicherungswirtschaft, Karlsruhe.Google Scholar
Hull, J.C. (1997). Options, futures, and other derivatives. International Edition. Prentice-Hall.Google Scholar
Kahn, P.M. (1971). Projections of variable life insurance operations, with discussion. Transactions of the Society of Actuaries, XXIII, 335–366.Google Scholar
Lamberton, D. & Lapeyre, B. (1996). Introduction to stochastic calculus applied to finance. Chapman & Hall.Google Scholar
Merton, R.C. (1973). Theory of rational option pricing. Bell Journal of Economics and Management Science, 4, 141–183.Google Scholar
Møller, T. (1998). Risk-minimising hedging strategies for unit-linked life insurance contracts. ASTIN Bulletin, 28, 17–47.CrossRefGoogle Scholar
Møller, T. (2001a). Hedging equity-linked life insurance contracts. North American Actuarial Journal, 5(2), 79–95.CrossRefGoogle Scholar
Møller, T. (2001b). On transformations of actuarial valuation principles. Insurance: Mathematics and Economics, 28, 281–303.Google Scholar
Møller, T. (2001c). Risk-minimising hedging strategies for insurance payment processes. Finance and Stochastics, 5, 419–446.Google Scholar
Møller, T. (2002a). Indifference pricing of insurance contracts in a product space model: applications. Preprint, Laboratory of Actuarial Mathematics, University of Copenhagen.Google Scholar
Møller, T. (2002b). Indifference pricing of insurance contracts in a product space model. Finance and Stochastics (to appear).CrossRefGoogle Scholar
Nielsen, J. & Sandmann, K. (1995). Equity-linked life insurance: a model with stochastic interest rates. Insurance: Mathematics and Economics, 16, 225–253.Google Scholar
Norberg, R. (1999). A theory of bonus in life insurance. Finance and Stochastics, 3, 373–390.CrossRefGoogle Scholar
Norberg, R. (2000). Basic life insurance mathematics. Lecture notes, Laboratory of Actuarial Mathematics, University of Copenhagen.Google Scholar
Persson, S.A. (1998). Stochastic interest in life insurance: the principle of equivalence revisited Scandinavian Actuarial Journal, 97–112.CrossRefGoogle Scholar
Ramlau-Hansen, H. (1991). Distribution of surplus in life insurance. ASTIN Bulletin, 21, 57–71.CrossRefGoogle Scholar
Samuelson, P.A. (1965). Rational theory of warrant pricing. Industrial Management Review, 6, 13–31.Google Scholar
Schmock, U. (1999). Estimating the value of the WinCAT coupons of the Winterthur Insurance convertible bond: a study of the model risk. ASTIN Bulletin, 29, 101–163.CrossRefGoogle Scholar
Schweizer, M. (1988). Hedging of options in a general semimartingale model, Diss. ETHZ no. 8615, Zürich.Google Scholar
Schweizer, M. (1991). Option hedging for semimartingales. Stochastic Processes and their Applications, 37, 339–363.CrossRefGoogle Scholar
Schweizer, M. (2001a). A guided tour through quadratic hedging approaches. In Jouini, E., Cvitanić, J. & Musiela, M. (eds), Option pricing, interest rates and risk management. Cambridge University Press, 538–574.CrossRefGoogle Scholar
Schweizer, M. (2001b). From actuarial to financial valuation principles. Insurance: Mathematics and Economics, 28, 31–47.Google Scholar
Sondermann, D. (1991). Reinsurance in arbitrage-free markets. Insurance: Mathematics and Economics, 10, 191–202.Google Scholar
Squires, R.J. (1986). Unit linked business. Life assurance monograph, Institute of Actuaries and Faculty of Actuaries.Google Scholar
Steffensen, M. (2000). A no arbitrage approach to Thiele's differential equation. Insurance: Mathematics and Economics, 27, 201–214.Google Scholar
Steffensen, M. (2001). On valuation and control in life and pension insurance. Ph.D. thesis, University of Copenhagen.Google Scholar
Swiss Re (1998). Integrated risk management solutions — beyond traditional reinsurance and financial hedging. Internal paper, Swiss Re New Markets, Zürich.Google Scholar
Tilley, J.A. (1997). The securitization of catastrophic property risks. Proceedings of the 7th AFIR Colloquium and the 28th ASTIN Colloquium, Cairns, Joint Day Vol., 27–53.Google Scholar
Turner, S.H. (1969). Asset value guarantees under equity-based products, with discussion. Transactions of the Society of Actuaries, XXI, 459–493.Google Scholar
Turner, S.H. (1971). Equity-based life insurance in the United Kingdom, with discussion. Transactions of the Society of Actuaries, XXIII, 273–324.Google Scholar
Wilkie, A.D. (1978). Maturity (and other) guarantees under unit linked policies. T.F.A. 36, 27–41.Google Scholar