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The design of pension contracts: on the perspective of customers

  • Zhaoxun Mei (a1)

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.

Corresponding author
*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:
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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), 616637.
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), 269290.
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), 275297.
Bauer, D., Kiesel, R., Kling, A. & Ruß, J. (2006). Risk-neutral valuation of participating life insurance contracts. Insurance: Mathematics and Economics, 39(2), 171183.
Black, F. & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81(3), 637654.
Branger, N., Mahayni, A. & Schneider, J.C. (2010). On the optimal design of insurance contracts with guarantees. Insurance: Mathematics and Economics, 46(3), 485492.
Bruhn, K. & Steffensen, M. (2013). Optimal smooth consumption and annuity design. Journal of Banking & Finance, 37(8), 26932701.
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, 327339.
Choquet, G. (1954). Theory of capacities. Annales de l’institut Fourier, 5, 131295.
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), 16831697.
Døskeland, T.M. & Nordahl, H.A. (2008 a). Intergenerational effects of guaranteed pension contracts. The Geneva Risk and Insurance Review, 33(1), 1946.
Døskeland, T.M. & Nordahl, H.A. (2008 b). Optimal pension insurance design. Journal of Banking & Finance, 32(3), 382392.
Ellsberg, D. (1961). Risk, ambiguity, and the savage axioms. The Quarterly Journal of Economics, 75(4), 643669.
Grosen, A. & Jørgensen, P.L. (1997). Valuation of early exercisable interest rate guarantees. Journal of Risk and Insurance, 64(3), 481503.
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), 3757.
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), 229252.
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.
Hansen, M. & Miltersen, K.R. (2002). Minimum rate of return guarantees: the Danish case. Scandinavian Actuarial Journal, 2002(4), 280318.
Harrison, J.M. & Kreps, D.M. (1979). Martingales and arbitrage in multiperiod securities markets. Journal of Economic Theory, 20(3), 381408.
Hens, T. & Rieger, M.O. (2014). Can utility optimization explain the demand for structured investment products? Quantitative Finance, 14(4), 673681.
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), 137152.
Kahneman, D. & Kahneman, A. (1979). Prospect theory: an analysis of decision under risk. Econometrica: Journal of the Econometric Society, 47(2), 263291.
Linnemann, P., Bruhn, K. & Steffensen, M. (2015). A comparison of modern investment-linked pension savings products. Annals of Actuarial Science, 9(1), 7284.
Merton, R.C. (1969). Lifetime portfolio selection under uncertainty: the continuous-time case. The Review of Economics and Statistics, 51(3), 247257.
Prelec, D. (1998). The probability weighting function. Econometrica, 66(3), 497527.
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), 467482.
Tversky, A. & Kahneman, D. (1992). Advances in prospect theory: cumulative representation of uncertainty. Journal of Risk and Uncertainty, 5(4), 297323.
Von Neumann, J. & Morgenstern, O. (1944). Theory of Games and Economic Behavior. Princeton University Press, Princeton, NJ.
Zemp, A. (2011). Risk comparison of different bonus distribution approaches in participating life insurance. Insurance: Mathematics and Economics, 49(2), 249264.
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Annals of Actuarial Science
  • ISSN: 1748-4995
  • EISSN: 1748-5002
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