Abstract
This paper develops life insurance pricing with stochastic representation of mortality and fuzzy quantification of interest rates following the methodology by Andrés and González-Vila (2012). We show that modelling the present value of life insurance contracts with fuzzy random variables allows a well-founded quantification of their fair price and the risk resulting from the uncertainty of mortality and discounting rates. So, we firstly describe fuzzy random variables and define some associated measures: the mathematical expectation, the variance, distribution function and quantiles. Subsequently the present value of life insurance policies is modelled with fuzzy random variables. We finally show how an actuary can quantify the price and the risk of a life insurance portfolio when the contracts present value is given by fuzzy random variables.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alegre, A., Claramunt, M.M.: Allocation of solvency cost in group annuities: Actuarial principles and cooperative game theory. Insurance: Mathematics and Economic 17, 19–34 (1995)
de Andrés, J., González-Vila, L.: Using fuzzy random variables in life annuities pricing. Fuzzy Sets and Systems 188, 27–44 (2012)
de Andrés, J., Terceño, A.: Applications of Fuzzy Regression in Actuarial Analysis. Journal of Risk and Insurance 70, 665–699 (2003)
Betzuen, A., Jiménez, M., Rivas, J.A.: Actuarial mathematics with fuzzy parameters. An application to collective pension plans. Fuzzy Economic Review 2, 47–66 (1997)
Buckley, J.J.: The fuzzy mathematics of finance. Fuzzy Sets and Systems 21, 57–73 (1987)
Couso, I., Dubois, D., Montes, S., Sánchez, L.: On various definitions of the variance of a fuzzy random variable. In: 5th International Symposium on Imprecise Probabilities and Their Applications, Prague, Czech Republic (2007)
Cummins, J.D., Derrig, R.A.: Fuzzy financial pricing of property-liability insurance. North American Actuarial Journal 1, 21–44 (1997)
Derrig, R.A., Ostaszewski, K.: Managing the tax liability of a property liability insurance com-pany. Journal of Risk and Insurance 64, 695–711 (1997)
Derrig, R.A., Ostaszewski, K.: Fuzzy Sets. In: Encyclopaedia of Actuarial Science, vol. 2, pp. 745–750. John Wiley & Sons, Chichester (2004)
Feng, Y., Hu, L., Shu, H.: The variance and covariance of fuzzy random variables and their applications. Fuzzy Sets and Systems 120, 487–497 (2001)
Gerber, H.U.: Life Insurance Mathematics. Springer, Berlin (1995)
Gil-Aluja, J.: Investment on uncertainty. Kluwer Academic Publishers, Dordretch (1998)
Guangyuan, W., Yue, Z.: The theory of fuzzy stochastic processes. Fuzzy Sets and Systems 51, 161–178 (1992)
Huang, T., Zhao, R., Tang, W.: Risk model with fuzzy random individual claim amount. European Journal of Operational Research 192, 879–890 (2009)
Kaufmann, A.: Fuzzy subsets applications in O.R. and management. In: Jones, A., Kaufmann, A., Zimmermann, H.J. (eds.) Fuzzy Set Theory and Applications, pp. 257–300. Reidel, Dordrecht (1986)
Kaufmann, A., Gil-Aluja, J.: Las matemáticas del azar y de la incertidumbre. Ceura, Madrid (1990)
Körner, R.: On the variance of fuzzy random variables. Fuzzy Sets and Systems 92, 83–93 (1997)
Krätschmer, V.: A unified approach to fuzzy random variables. Fuzzy Sets and Systems 123, 1–9 (2001)
Kruse, R., Meyer, K.D.: Statistics with vague data. Reidel, Dordrecht (1987)
Kwakernaak, H.: Fuzzy random variables I: Definitions and Theorems. Information Sciences 15, 1–29 (1978)
Kwakernaak, H.: Fuzzy random variables II: Algorithms and Examples for the Discrete Case. Information Sciences 17, 253–278 (1979)
Lemaire, J.: Fuzzy insurance. Astin Bulletin 20, 33–55 (1990)
Li Calzi, M.: Towards a general setting for the fuzzy mathematics of finance. Fuzzy Sets and Systems 35, 265–280 (1990)
Ostaszewski, K.: An investigation into possible applications of fuzzy sets methods in actuarial science. Society of Actuaries, Schaumburg (1993)
Pitacco, E.: Simulation in insurance. In: Goovaerts, M., De Vylder, F., Haezendonck, J. (eds.) Insurance and Risk Theory, pp. 43–44. Reidel, Dordrecht (1986)
Puri, M.L., Ralescu, D.A.: Fuzzy random variables. Journal of Mathematical Analysis and Applications 114, 409–422 (1986)
Shapiro, A.F.: Fuzzy logic in insurance. Insurance: Mathematics and Economics 35, 399–424 (2004)
Shapiro, A.F.: Fuzzy random variables. Insurance: Mathematics and Economics 44, 307–314 (2009)
Yakoubov, Y.H., Haberman, S.: Review of actuarial applications of fuzzy set theory. Actuarial Research Paper n. 105. Department of Actuarial Science and Statistics of the City University, London (1998)
Zhao, R., Govind, R.: Defuzzification of fuzzy intervals. Fuzzy Sets and Systems 43, 45–55 (1991)
Zhong, C., Zhou, G.: The equivalence of two definitions of fuzzy random variables. In: Proceedings of the 2nd IFSA Congress, Tokyo, pp. 59–62 (1987)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
de Andrés-Sánchez, J., González-Vila Puchades, L. (2012). A Fuzzy Random Variable Approach to Life Insurance Pricing. In: Gil-Lafuente, A., Gil-Lafuente, J., Merigó-Lindahl, J. (eds) Soft Computing in Management and Business Economics. Studies in Fuzziness and Soft Computing, vol 287. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30451-4_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-30451-4_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-30450-7
Online ISBN: 978-3-642-30451-4
eBook Packages: EngineeringEngineering (R0)