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Pricing guaranteed life insurance participating policies with annual premiums and surrender option. (English) Zbl 1084.62519

Summary: This paper analyzes a life insurance endowment policy, paid by annual premiums, in which the benefit is annually adjusted according to the performance of a special investment portfolio and a minimum return is guaranteed to the policyholder. In particular, the author considers both the case in which the annual premium is constant and the case in which the premium also is adjusted according to the performance of the reference portfolio. Moreover, the policy under scrutiny is characterized by the presence of a surrender option, that is, of an American-style put option that enables the policyholder to give up the contract and receive the surrender value. The aim of the paper is to give sufficient conditions under which there exists a (unique) fair premium. This premium is implicitly defined by an equation (or, alternatively, can be viewed as a fixed point of a suitable function) based on a recursive binomial tree a la Cox, Ross, and Rubinstein (1979). An iterative algorithm is then implemented in order to compute it.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
91B30 Risk theory, insurance (MSC2010)
91G20 Derivative securities (option pricing, hedging, etc.)
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References:

[1] Albizzati M.-O., Journal of Risk and Insurance 61 (4) pp 616– (1994)
[2] Babbel D.F., North American Actuarial Journal 2 (3) pp 1– (1998) · Zbl 1081.62559
[3] Bacinello A.R., ASTIN Bulletin 31 (2) pp 275– (2001) · Zbl 1098.91537
[4] Bacinello A.R., Journal of Risk and Insurance 70 (3) pp 461– (2003)
[5] Bacinello A.R., Journal of Risk Finance 3 (2) pp 6– (2002)
[6] Black F., Journal of Political Economy 81 (3) pp 637– (1973) · Zbl 1092.91524
[7] Booth R., Modern Actuarial Theory and Practice (1999) · Zbl 0935.62117
[8] Bowers N.L., Actuarial Mathematics (1997)
[9] Boyle P.P., North American Actuarial Journal 5 (3) pp 1– (2001) · Zbl 1083.91511
[10] Boyle P.P., Journal of Risk and Insurance 44 (4) pp 639– (1977)
[11] Brennan M.J., Journal of Financial Economics 3 pp 195– (1976)
[12] Briys E., Geneva Papers on Risk and Insurance Theory 19 (1) pp 53– (1994)
[13] Briys E., Journal of Risk and Insurance 64 (4) pp 673– (1997)
[14] Briys E., Insurance from Underwriting to Derivatives. Asset Liability Management in Insurance Companies (2001) · Zbl 1076.91022
[15] Consiglio A., Journal of Risk Finance 2 (3) pp 6– (2001)
[16] Consiglio A., Asset and Liability Modeling for Participating Policies with Guarantees (2001) · Zbl 1138.91491
[17] Cox J.C., Journal of Financial Economics 7 pp 229– (1979) · Zbl 1131.91333
[18] Cox S.H., North American Actuarial Journal 4 (4) pp 56– (2000) · Zbl 1083.91534
[19] Grosen A., Journal of Risk and Insurance 64 (3) pp 481– (1997)
[20] Grosen A., Insurance: Mathematics & Economics 26 (1) pp 3– (2000) · Zbl 0977.62108
[21] Grosen A., Journal of Risk and Insurance 69 (1) pp 63– (2002)
[22] Hansen M., Scandinavian Actuarial Journal pp 280– (2002) · Zbl 1039.91040
[23] Jensen B., Geneva Papers on Risk and Insurance Theory 26 (1) pp 57– (2001)
[24] Merton R.C., Bell Journal of Economics and Management Science 4 pp 141– (1973)
[25] Miltersen K.R., Scandinavian Actuarial Journal (2000)
[26] Møller T., ASTIN Bulletin 28 (1) pp 17– (1998) · Zbl 1168.91417
[27] Møller T., North American Actuarial Journal 5 (2) pp 79– (2001) · Zbl 1083.91546
[28] Møller T., Finance and Stochastics 5 pp 419– (2001) · Zbl 0983.62076
[29] Norberg R., Finance and Stochastics 3 pp 373– (1999) · Zbl 0939.62108
[30] Norberg R., Scandinavian Actuarial Journal pp 126– (2001) · Zbl 0979.91045
[31] Pacati C., Valutazione di Portafogli di Polizze Vita con Rivalutazione agli Ennesimi (2000)
[32] Pliska S.R., Introduction to Mathematical Finance: Discrete Time Models (1997)
[33] Steffensen M., Insurance: Mathematics & Economics 31 (1) pp 71– (2002) · Zbl 1013.62103
[34] Tiong S., North American Actuarial Journal 4 (4) pp 149– (2000) · Zbl 1083.62545
[35] Wilkie A.D., Journal of the Institute of Actuaries 114 pp 21– (1987)
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