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The design of pension contracts: on the perspective of customers

Published online by Cambridge University Press:  18 June 2018

Zhaoxun Mei
Zhaoxun Mei*
Affiliation:
Actuarial Mathematics and Statistics, Heriot Watt University, G.11 Colin Maclaurin Building, Edinburgh EH14 4AS, UK
*
*Correspondence to: Zhaoxun Mei, Actuarial Mathematics and Statistics, Heriot Watt University, G.11 Colin Maclaurin Building, Edinburgh EH14 4AS, UK. Tel: +44 1314 513235; E-mail: [email protected]
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Abstract

This paper introduces a new pension contract which provides a smoothed return for the customer. The new contract protects customers from adverse asset price movements while keeping the potential of positive returns. It has a transparent structure and clear distribution rule, which can be easily understood by the customer. We compare the new contract to two other contracts under Cumulative Prospect Theory (CPT); one has a similar product structure but without guarantees and the other provides the same guarantee rate but with a different structure. The results show that the new contract is the most attractive contract for a CPT-maximising customer. Yet, we find different results if we let the customer be an Expected Utility Theory-maximising one. Moreover, this paper presents the static optimal portfolio for an individual customer. The results conform to the traditional pension advice that young people should invest more of their money in risky assets while older people should put more money in less risky assets.

Keywords

Cumulative Prospect TheoryLife and pension insuranceProduct designPortfolio choice
Type
Paper
Information
Annals of Actuarial Science , Volume 13 , Issue 2 , September 2019 , pp. 219 - 240
Copyright
© Institute and Faculty of Actuaries 2018 

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References

Albizzati, M.-O. & Geman, H. (1994). Interest rate risk management and valuation of the surrender option in life insurance policies. Journal of Risk and Insurance, 61(4), 616–637.Google Scholar
Allais, M. (1953). L’extension des théories de l’équilibre économique général et du rendement social au cas du risque. Econometrica, Journal of the Econometric Society, 21(4), 269–290.Google Scholar
Bacinello, A.R. (2001). Fair pricing of life insurance participating policies with a minimum interest rate guaranteed. ASTIN Bulletin: The Journal of the IAA, 31(2), 275–297.Google Scholar
Bauer, D., Kiesel, R., Kling, A. & Ruß, J. (2006). Risk-neutral valuation of participating life insurance contracts. Insurance: Mathematics and Economics, 39(2), 171–183.Google Scholar
Black, F. & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81(3), 637–654.Google Scholar
Branger, N., Mahayni, A. & Schneider, J.C. (2010). On the optimal design of insurance contracts with guarantees. Insurance: Mathematics and Economics, 46(3), 485–492.Google Scholar
Bruhn, K. & Steffensen, M. (2013). Optimal smooth consumption and annuity design. Journal of Banking & Finance, 37(8), 2693–2701.Google Scholar
Chen, A., Hentschel, F. & Klein, J.K. (2015). A utility-and CPT-based comparison of life insurance contracts with guarantees. Journal of Banking & Finance, 61, 327–339.Google Scholar
Choquet, G. (1954). Theory of capacities. Annales de l’institut Fourier, 5, 131–295.Google Scholar
Dichtl, H. & Drobetz, W. (2011). Portfolio insurance and prospect theory investors: popularity and optimal design of capital protected financial products. Journal of Banking & Finance, 35(7), 1683–1697.Google Scholar
Døskeland, T.M. & Nordahl, H.A. (2008 a). Intergenerational effects of guaranteed pension contracts. The Geneva Risk and Insurance Review, 33(1), 19–46.Google Scholar
Døskeland, T.M. & Nordahl, H.A. (2008 b). Optimal pension insurance design. Journal of Banking & Finance, 32(3), 382–392.Google Scholar
Ellsberg, D. (1961). Risk, ambiguity, and the savage axioms. The Quarterly Journal of Economics, 75(4), 643–669.Google Scholar
Grosen, A. & Jørgensen, P.L. (1997). Valuation of early exercisable interest rate guarantees. Journal of Risk and Insurance, 64(3), 481–503.Google Scholar
Grosen, A. & Jørgensen, P.L. (2000). Fair valuation of life insurance liabilities: the impact of interest rate guarantees, surrender options, and bonus policies. Insurance: Mathematics and Economics, 26(1), 37–57.Google Scholar
Guilléen, M., Jørgensen, P.L. & Nielsen, J.P. (2006). Return smoothing mechanisms in life and pension insurance: path-dependent contingent claims. Insurance: Mathematics and Economics, 38(2), 229–252.Google Scholar
Haberman, S., Ballotta, L. & Wang, N. (2003). Modelling and valuation of guarantees in with-profit and unitised with profit life insurance contracts, Actuarial Research Paper No. 146, Cass Business School, City of London.Google Scholar
Hansen, M. & Miltersen, K.R. (2002). Minimum rate of return guarantees: the Danish case. Scandinavian Actuarial Journal, 2002(4), 280–318.Google Scholar
Harrison, J.M. & Kreps, D.M. (1979). Martingales and arbitrage in multiperiod securities markets. Journal of Economic Theory, 20(3), 381–408.Google Scholar
Hens, T. & Rieger, M.O. (2014). Can utility optimization explain the demand for structured investment products? Quantitative Finance, 14(4), 673–681.Google Scholar
Jørgensen, P.L. & Linnemann, P. (2012). A comparison of three different pension savings products with special emphasis on the payout phase. Annals of Actuarial Science, 6(1), 137–152.Google Scholar
Kahneman, D. & Kahneman, A. (1979). Prospect theory: an analysis of decision under risk. Econometrica: Journal of the Econometric Society, 47(2), 263–291.Google Scholar
Linnemann, P., Bruhn, K. & Steffensen, M. (2015). A comparison of modern investment-linked pension savings products. Annals of Actuarial Science, 9(1), 72–84.Google Scholar
Merton, R.C. (1969). Lifetime portfolio selection under uncertainty: the continuous-time case. The Review of Economics and Statistics, 51(3), 247–257.Google Scholar
Prelec, D. (1998). The probability weighting function. Econometrica, 66(3), 497–527.Google Scholar
Samuelson, P.A. (1958). An exact consumption-loan model of interest with or without the social contrivance of money. The Journal of Political Economy, 66(6), 467–482.Google Scholar
Tversky, A. & Kahneman, D. (1992). Advances in prospect theory: cumulative representation of uncertainty. Journal of Risk and Uncertainty, 5(4), 297–323.Google Scholar
Von Neumann, J. & Morgenstern, O. (1944). Theory of Games and Economic Behavior. Princeton University Press, Princeton, NJ.Google Scholar
Zemp, A. (2011). Risk comparison of different bonus distribution approaches in participating life insurance. Insurance: Mathematics and Economics, 49(2), 249–264.Google Scholar