Pricing insurance contracts under Cumulative Prospect Theory

The aim of this paper is to introduce a premium principle which relies on Cumulative Prospect Theory by Kahneman and Tversky. Some special cases of this premium principle have already been studied in the actuarial literature. In the paper, properties of this premium principle are examined.

[1]  Stoyan V. Stoyanov,et al.  Distortion Risk Measures in Portfolio Optimization , 2010 .

[2]  H. Gerber.  On additive principles of zero utility , 1985 .

[3]  Attila Gilányi,et al.  An Introduction to the Theory of Functional Equations and Inequalities , 2008 .

[4]  M. Goovaerts,et al.  A note on additive risk measures in rank-dependent utility , 2010 .

[5]  S. Heilpern.  A rank-dependent generalization of zero utility principle , 2003 .

[6]  A. Tversky,et al.  Advances in prospect theory: Cumulative representation of uncertainty , 1992 .

[7]  Hans U. Gerber,et al.  An introduction to mathematical risk theory , 1982 .

[8]  P. Wakker.  Prospect Theory: For Risk and Ambiguity , 2010 .

[9]  Joshua C. Teitelbaum.  A Unilateral Accident Model under Ambiguity , 2007, The Journal of Legal Studies.

[10]  H. J. Einhorn,et al.  Expression theory and the preference reversal phenomena. , 1987 .

[11]  J. Guerard.  Handbook of portfolio construction : contemporary applications of Markowitz techniques , 2010 .

[12]  M. Kaluszka,et al.  An Extension of Arrow's Result on Optimal Reinsurance Contract , 2008 .

[13]  Shaun S. Wang,et al.  Insurance pricing and increased limits ratemaking by proportional hazards transforms , 1995 .

[14]  A. Tversky,et al.  Prospect theory: analysis of decision under risk , 1979 .

[15]  R. Sugden,et al.  Third-generation prospect theory , 2008 .

[16]  Andreas Tsanakas,et al.  To Split or Not to Split: Capital Allocation with Convex Risk Measures , 2007 .

[17]  M. Sherris,et al.  A class of non-expected utility risk measures and implications for asset allocations , 2001 .

[18]  Qihe Tang,et al.  A Comonotonic Image of Independence for Additive Risk Measures , 2004 .

[19]  Ulrich Schmidt,et al.  Linear cumulative prospect theory with applications to portfolio selection and insurance demand , 2002 .

[20]  Ulrich Schmidt,et al.  Parametric weighting functions , 2009, J. Econ. Theory.

[21]  M. Rabin,et al.  Reference-Dependent Risk Attitudes , 2007 .

[22]  A. Tversky,et al.  Prospect Theory : An Analysis of Decision under Risk Author ( s ) : , 2007 .

[23]  A. V. Manzhirov,et al.  Handbook of mathematics for engineers and scientists , 2006 .

[24]  J. Quiggin.  A theory of anticipated utility , 1982 .

[25]  D. Prelec.  The Probability Weighting Function , 1998 .

[26]  Shaun S. Wang.  Premium Calculation by Transforming the Layer Premium Density , 1996, ASTIN Bulletin.

[27]  A Taxonomy of Utility Functions , 2008 .

[28]  Uzi Segal.  Anticipated utility: A measure representation approach , 1989 .