Abstract
We deal with the problem of pricing equity-linked life insurance policies under uncertainty of randomness and fuzziness. Firstly, we propose an evaluation method for general life insurance, with stochastic representation of mortality and fuzzy quantification of financial present values, by defining the actuarial value of the liabilities as the expectation of a fuzzy random variable. Then, we apply the suggested methodology to the fair valuation of an equity-linked policy. In such a contract policyholder’s benefits are linked to the performance of a reference fund. We perform the risk neutral valuation in a fuzzy binomial-tree model. The crisp value of the policy is obtained by means of a “defuzzification method” based on possibilistic mean values. A numerical example illustrates how the proposed method allows the actuary to model the fuzziness in the parameters according to his subjective judgement.
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References
Zadeh, L.A.: Fuzzy sets. Inform. Control 8, 338–353 (1965)
Lemaire, J.: Fuzzy insurance. ASTIN Bull. 20, 33–55 (1990)
Terceno, A., De Andres, J., Belvis, C., Barbera, G.: Fuzzy methods incorporated to the study of personal insurances. In: Int. Symp. Neuro-Fuzzy Syst., pp. 187–202 (1996)
Ostaszewski, K.: An Investigation into Possible Applications of Fuzzy Sets Methods in Actuarial Science. Society of Actuaries, Schaumburg (1993)
Buckley, J.J.: The fuzzy mathematics of finance. Fuzzy Sets and Systems 21, 257–273 (1987)
Shapiro, A.F.: Fuzzy logic in insurance. Insurance: Mathematics and Economics 35, 399–424 (2004)
Hardy, M.: Investment guarantees: Modelling and risk management for equity-linked life insurance. Wiley (2003)
Brennan, M.J., Schwartz, E.S.: The pricing of equity-linked life insurance policies with an asset value guarantee. J. Finan. Econ. 3, 195–213 (1976)
Hull, J.C.: Options, Futures, and Other Derivatives. Prentice Hall (2003)
Cox, J.C., Ross, S.A., Rubinstein, M.: Option Pricing: A Simplified Approach. Journal of Financial Economics 7, 229–263 (1979)
Kwakernaak, H.: Fuzzy random variables. Part I: definitions and theorems. Inform. Sci. 15, 1–29 (1978)
Kwakernaak, H.: Fuzzy random variables. Part II: algorithms and examples for the discrete case. Inform. Sci. 17, 253–278 (1979)
Kruse, R., Meyer, K.D.: Statistics with Vague Data. Reidel Publ. Co. (1987)
Puri, M.L., Ralescu, D.A.: Fuzzy random variables. Journal of Mathematical Analysis and Applications 114, 409–422 (1986)
de Andrés-Sánchez, J., González-Vila Puchades, L.: Using fuzzy random variables in life annuities pricing. Fuzzy Sets and Systems 188, 27–44 (2012)
Carlsson, C., Fuller, R.: On possibilistic mean value and variance of fuzzy numbers. Fuzzy Sets and Systems 122, 315–326 (2001)
Fuller, R., Majlender, P.: On weighted possibilistic mean and variance of fuzzy numbers. Fuzzy Sets and Systems 136, 363–374 (2003)
Bodjanova, S.: Median value and median interval of a fuzzy number. Information Sciences 172, 73–89 (2005)
Gil, M.Á., López-Díaz, M., Ralescu, D.A.: Overview on the Development of Fuzzy Random Variables. Fuzzy Sets and Systems 157, 2546–2557 (2006)
Gerber, H.U.: Life Insurance Mathematics. Springer, Berlin (1995)
Kaufmann, A., Gupta, M.M.: Introduction to fuzzy arithmetic. Theory and applications. Van Nostrand Reinhold Company Inc. (1985)
Muzzioli, S., Torricelli, C.: A multiperiod binomial model for pricing options in a vague world. Journal of Economic Dynamics and Control 28, 861–887 (2004)
Muzzioli, S., Reynaerts, H.: The solution of fuzzy linear systems by non linear programming: a financial application. European Journal of Operational Research 177, 1218–1231 (2007)
Muzzioli, S., Reynaerts, H.: American option pricing with imprecise risk-neutral probabilities. International Journal of Approximate Reasoning 49, 140–147 (2008)
Yoshida, Y.: A discrete-time model of American put option in an uncertain environment. European Journal of Operational Research 151, 153–166 (2003)
Buckley, J.J., Qu, Y.: Solving systems of linear fuzzy equations. Fuzzy Sets and Systems 43, 33–43 (1991)
Melnikov, A.: Risk Analysis in Finance and Insurance. Chapman & Hall (2003)
Bacinello, A.R.: Endogenous model of surrender conditions in equity-linked life insurance. Insurance: Mathematics and Economics 37, 270–296 (2005)
Zadeh, L.A.: A fuzzy-set-theoretic interpretation of linguistic hedge. Journal of Cybernetics 2, 4–34 (1972)
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Anzilli, L. (2012). A Possibilistic Approach to Evaluating Equity-Linked Life Insurance Policies. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds) Advances in Computational Intelligence. IPMU 2012. Communications in Computer and Information Science, vol 300. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31724-8_6
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DOI: https://doi.org/10.1007/978-3-642-31724-8_6
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