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Ambiguity Aversion: A New Perspective on Insurance Pricing

Published online by Cambridge University Press:  09 August 2013

Lin Zhao  and
Wei Zhu
Lin Zhao
Affiliation:
China Center for Insurance and Risk Management, School of Economics and Management, Tsinghua University, Beijing, 100084, PRC., E-Mail: [email protected]
Wei Zhu
Affiliation:
School of Insurance and Economics, University of International Business and Economics, Beijing, 100029, PRC., E-Mail: [email protected]
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Abstract

This paper intends to develop a feasible framework which incorporates ambiguity aversion into the pricing of insurance products and investigate the implications of ambiguity aversion on the pricing by comparing it with risk aversion. As applications of the framework, we present the closed-form pricing formulae for some insurance products appearing in life insurance and property insurance. Our model confirms that the effects of ambiguity aversion on the pricing of insurance do differ from those of risk aversion. Implications of our model are consistent with some empirical evidences documented in the literature. Our results suggest that taking advantage of natural hedge mechanism can help us control the effects of model uncertainty.

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 41 , Issue 1 , May 2011 , pp. 157 - 189
Copyright
Copyright © International Actuarial Association 2011

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References

Anderson, E., Hansen, L. and Sargent, T. (1999) Robustness, Detection and the Price of Risk, working paper, University of North Carolina, University of Chicago, and Stanford University.Google Scholar
Artzner, P., Delbaen, F., Eber, J. and Heath, D. (1999) Coherent Measures of Risk, Mathematical Finance, 9: 203–228.CrossRefGoogle Scholar
Bayraktar, E. and Young, V.R. (2007) Hedging Life Insurance with Pure Endowments, Insurance: Mathematics and Economics, 40: 435–444.Google Scholar
Biffis, E. (2005) Affine Processes for Dynamic Mortality and Actuarial Valuations, Insurance: Mathematics and Economics, 37: 443–468.Google Scholar
Cairns, A.J., Blake, D. and Dowd, K. (2006) Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk, ASTIN Bulletin, 36: 79–120.CrossRefGoogle Scholar
Cairns, A.J., Blake, D. and Dowd, K. (2008) Modeling and Management of Mortality Risk: A Review, Scandinavian Actuarial Journal, 2–3: 79–113.CrossRefGoogle Scholar
Chen, B.Z., Zhang, L.H. and Zhao, L. (2010) On the Robustness of Longevity Risk Pricing, Insurance: Mathematics and Economics, forthcoming.Google Scholar
Chen, Z. and Epstein, L. (2002) Ambiguity, Risk and Asset Returns in Continuous Time, Econometrica, 70: 1403–1443.CrossRefGoogle Scholar
Cox, H., Fairchild, J. and Pedersen, H. (2004) Valuation of Structured Risk Management Products, Insurance: Mathematics and Economics, 34: 259–272.Google Scholar
Cox, H. and Lin, Y. (2007) Natural Hedging of Life and Annuity Mortality Risks, North American Actuarial Journal, 11: 1–15.CrossRefGoogle Scholar
Cox, H., Lin, Y. and Wang, S.S. (2006) Multivariate Exponential Tilting and Pricing Implications for Mortality Securitization, Journal of Risk and Insurance, 73: 719–736.CrossRefGoogle Scholar
Cummins, J.D. and Geman, H. (1995) Pricing Catastrophe Futures and Call Spreads: An Arbitrage Approach, Journal of Fixed Income, 4: 46–57.CrossRefGoogle Scholar
Dahl, M. (2004) Stochastic Mortality in Life Insurance: Market Reserves and Mortality-Linked Insurance Contracts, Insurance: Mathematics and Economics, 35: 113–136.Google Scholar
Davis, M.H.A., Panas, V.G. and Zarphipoulou, T. (1993) European Option Pricing with Transaction Costs, SIAM Journal on Control and Optimization, 31: 470–493.CrossRefGoogle Scholar
Delbaen, F. (2002) Coherent Risk Measures of Risk on General Probability Spaces, Advances in Finance and Stochastics, Sandmann, K. and Schönbucher, P., eds. New York: Springer-Verlag.Google Scholar
Earthquake Project (1990) Catastrophic Earthquakes: The Need to Insure Against Economic Disaster, Boston: National Committee on Property Insurance.Google Scholar
Egami, M. and Young, V.R. (2008) Indifference Prices of Structured Catastrophe (CAT) Bonds, Insurance: Mathematics and Economics, 42: 771–778.Google Scholar
El Karoui, N. (2009) Cash Subadditivity Risk Measures and Interests Rate Uncertainty, Mathematical Finance, 19: 561–590.CrossRefGoogle Scholar
Ellsberg, D. (1961) Risk, ambiguity and the Savage axioms, Quarterly Journal of Economics, 75: 643–669.CrossRefGoogle Scholar
Epstein, L. and Wang, T. (1994) Intertemporal Asset Pricing under Knightian Uncertainty, Econometrica, 62: 283–322.CrossRefGoogle Scholar
Föllmer, H. and Schied, A. (2002) Stochastic Finance: An Introduction in Discrete Time, De Gruyter Studies in Mathematics, Berlin, Germany.CrossRefGoogle Scholar
Froot, K.A. (2001) The Market for Catastrophe Risk: A Clinical Examination, Journal of Financial Economics, 60: 529–571.CrossRefGoogle Scholar
Frittelli, M. (2000) Representing Sublinear Risk Measures and Pricing Rules, working paper, Univesiá Bicocca di Milano, Italy.Google Scholar
Frittelli, M. and Rosazza Gianin, E. (2002) Putting Order in Risk Measures, Journal of Banking and Finance, 26: 1473–1486.CrossRefGoogle Scholar
Garlappi, L., Uppal, R. and Wang, T. (2007) Portfolio Selection with Parameter and Model Uncertainty: A Multi-Prior Approach, Review of Financial Studies, 20: 42–81.CrossRefGoogle Scholar
Gerber, H. (1974) On Additive Premium Calculation Principles, ASTIN Bulletin, 7: 215–222.CrossRefGoogle Scholar
Gilboa, I. and Schmeidler, D. (1989) Maxmin Expected Utility Theory with Non-unique Prior, Journal of Mathematical Economics, 18: 141–153.CrossRefGoogle Scholar
Goldfarb, D. and Iyengar, G. (2003) Robust Portfolio Selection Problems, Mathematics of Operations Research, 28: 1–38.CrossRefGoogle Scholar
Hansen, L., Sargent, T. and Tallarini, T. (1999) Robust Permanent Income and Pricing, Review of Economic Studies, 66: 873–907.CrossRefGoogle Scholar
Hansen, L. and Sargent, T. (2001) Robust Control and Model Uncertainty, American Economic Review, 91: 60–66.CrossRefGoogle Scholar
Hodges, S.D. and Neuberger, A. (1989) Optimal Replication of Contingent Claims under Transaction Costs, Review of Futures Markets, 8: 222–239.Google Scholar
Ibragimov, R., Jaffee, D. and Walden, J. (2009) Nondiversii cation Traps in Catastrophe Insurance Markets, Review of Financial Studies, 22(3): 959–993.CrossRefGoogle Scholar
Klibanoff, P., Marinacci, M. and Mukerji, S. (2005) A Smooth Model of Decision Making under Ambiguity, Econometrica, 73: 1849–1892.CrossRefGoogle Scholar
Klugman, S., Panjer, H. and Willmot, G. (2004) Loss Models: from Data to Decisions, John Wiley & Sons, Inc., Hoboken, New Jersey.Google Scholar
Kunreuther, H., Hogarth, R. and Meszaros, J. (1993) Insurer Ambiguity and Market Failure, Journal of Risk and Uncertainty, 7: 71–87.CrossRefGoogle Scholar
Knight, F.H. (1921) Risk, Uncertainty, and Profit, Boston, MA: Hart, Schaffner & Marx; Houghton Mifflin Company.Google Scholar
Lee, J.P. and Yu, M.T. (2002) Pricing Default-Risky CAT Bonds with Moral Hazard and Basis Risk, Journal of Risk and Insurance, 69: 25–44.CrossRefGoogle Scholar
Lin, S.K., Chang, C.C. and Powers, M.R. (2010) The Valuation of Contingent Capital with Catastrophe Risks, Insurance: Mathematics and Economics, in press.Google Scholar
Liu, J., Pan, J. and Wang, T. (2005) An Equilibrium Model of Rare-Event Premia and Its Implication for Option Smirks, Review of Financial Studies, 18: 131–164.CrossRefGoogle Scholar
Ludkovski, M. and Young, V.R. (2008) Indifference Pricing of Pure Endowments and Life Annuities under Stochastic Hazard and Interest Rates, Insurance: Mathematics and Economics, 42: 14–30.Google Scholar
Maenhout, P. (2001) Robust Portfolio Rules, Hedging and Asset Pricing, working paper, Finance Department, INSEAD.Google Scholar
Merton, R. (1976) Option Pricing When Underlying Stock Returns are Discontinuous, Journal of Financial Economics, 3: 125–144.CrossRefGoogle Scholar
Milevsky, M.A., Promislow, S.D. and Young, V.R. (2005) Financial Valuation of Mortality Risk via the Instantaneous Sharpe Ratio, working paper, York University and University of Michigan.Google Scholar
Miltersen, K.R. and Persson, S.A. (2005) Is Mortality Dead? Stochastic Force of Mortality Determined by No Arbitrage, working paper, University of Bergen.Google Scholar
Musiela, M. and Zariphopoulou, T. (2004) An Example of Indifference Prices under Exponential Preferences, Finance and Stochastics, 8: 229–239.CrossRefGoogle Scholar
Pathak, P. (2002) Notes on Robust Portfolio Choice, working paper, Havard University.Google Scholar
Rabin, M. (2000) Risk Aversion and Expected-Utility Theory: A Calibration Theorem, Econometrica, 68(5): 1281–1292.CrossRefGoogle Scholar
Schied, A. (2005) Optimal Investment for Robust Utility Functionals in Complete Market Models, Mathematics of Operations Research, 30: 750–764.CrossRefGoogle Scholar
Schied, A. (2006) Risk Measures and Robust Optimization Problems, Lecture Notes of the 8th Symposium on Probability and Stochastic Processes.CrossRefGoogle Scholar
Segal, U. and Spivak, A. (1988) Non-Expected Utility Risk Premiums: The Cases of Probability Ambiguity and Outcome Uncertainty, Journal of Risk and Uncertainty, 1: 333–347.CrossRefGoogle Scholar
Skiadas, C. (2003) Robust Control and Recursive Utility, Finance and Stochastics, 7: 475–489.CrossRefGoogle Scholar
Uppal, R. and Wang, T. (2003) Model Misspecii cation and Under-Diversification, Journal of Finance, 58, 2465–2486.CrossRefGoogle Scholar
Young, V.R. (2008) Pricing Life Insurance under Stochastic Mortality via the Instantaneous Sharpe Ratio, Insurance: Mathematics and Economics, 42: 691–703.Google Scholar
Young, V.R. and Zarphipoulou, T. (2002) Pricing Dynamic Insurance Risks Using the Principle of Equivalent Utility, Scandinavian Actuarial Journal, 4: 246–279.CrossRefGoogle Scholar
Young, V.R. (2004) Premium Principles, in: Teugels, J. and Sundt, B., eds., Encyclopedia of Actuarial Science, Vol. 3 (Chichester, UK: Wiley).Google Scholar