Hostname: page-component-77c89778f8-vpsfw Total loading time: 0 Render date: 2024-07-17T09:10:14.338Z Has data issue: false hasContentIssue false
  • English
  • Français

LIFE INSURANCE AND PENSION CONTRACTS I: THE TIME ADDITIVE LIFE CYCLE MODEL

Published online by Cambridge University Press:  03 November 2014

Knut K. Aase
Knut K. Aase*
Affiliation:
The Norwegian School of Economics, 5045 Bergen and Centre of Mathematics for Applications (CMA), University of Oslo
*
E-Mail: knut.aase@nhh.no
Get access Rights & Permissions [Opens in a new window]

Abstract

We analyze optimal consumption in the life cycle model by introducing life and pension insurance contracts. The model contains a credit market with biometric risk, and market risk via risky securities. This idealized framework enables us to clarify important aspects of life insurance and pension contracts. We find optimal pension plans and life insurance contracts where the benefits are state dependent. We compare these solutions both to the ones of standard actuarial theory, and to policies offered in practice. Implications of this include what role the insurance industry may play to improve welfare. The relationship between substitution of consumption and risk aversion is highlighted in the presence of a consumption puzzle. One problem related portfolio choice is discussed the horizon problem. Finally, we present some comments on longevity risk and cohort risk.

Keywords

The life cycle modelpension insuranceoptimal life insurancelongevity riskthe horizon problemconsumption puzzle
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 45 , Issue 1 , January 2015 , pp. 1 - 47
Copyright
Copyright © ASTIN Bulletin 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aase, K.K. (2009) The investment horizon problem: A resolution. Working paper no. 7, NHH, Institute of Finance and Management Science, Bergen Norway.Google Scholar
Aase, K.K. (2014a) Recursive utility using the stochastic maximum principle. Working paper, NHH, Department of Business and Management Science, Bergen, Norway.Google Scholar
Aase, K.K. (2014b) Life insurance and pension contracts II: The recursive life cycle model. Working paper, NHH, Department of Business and Management Science, Bergen, Norway.Google Scholar
Benth, F.E. and Karlsen, K.H. (2005) “A note on Merton's portfolio selection problem for the Schwartz mean reversion model. Stochastic Analysis and Applications, 23, 687–704.Google Scholar
Bernheim, B.D., Shleifer, A. and Summers, L. H. (1985) The Strategic Bequest Motive. Journal of Political Economy, 93, 1045–1076.Google Scholar
Bodie, Z. (2009) Are stocks the best investment of the long run? The Economics's Voice, February 2009.Google Scholar
Breeden, D. (1979) An intertemporal asset pricing model with stochastic consumption and investment opportunities. Journal of Financial Economics, 7, 265–296.Google Scholar
Cox, J.C. and Huang, C.F. (1989) Optimal consumption and portfolio rules when asset prices follow a diffusion proocess. Journal of Economic Theory, 49, 1, 33–83.Google Scholar
Delong, J.B. (2008) Stocks for the long run. The Economics's Voice, 5 (7): Art 2. Available at: http://www.bepress.com/ev/vol5/iss7/art2.Google Scholar
Devolder, P. and Hainaut, D. (2006) The annuity puzzle revisited: A deterministic version with Lagrangian methods. Belgian Actuarial Bulletin, 6 (1), 40–48.Google Scholar
Dew-Becker, I. and Giglio, S. (2013) Asset pricing in the frequency domain: Theory and empirics. NBER Working Paper 19416.Google Scholar
Eberlein, E. and Madan, D.B. (2010) Unlimited liabillities, reserve capital requirements and the taxpayer put option. Working Paper, Freiburg Institute for Advanced Studies and University of Maryland.Google Scholar
Fisher, L. (1930) The Theory of Interest: As Determined by Impatience to Spend Income and Opportunity to Invest it. New York: Mac Millan.Google Scholar
Fisher, S. (1973) A life cycle model of life insurance purchases. International Economics Review, 14 (1), 132–152.Google Scholar
Hakansson, N.H. (1969) Optimal investment and consumption strategies under risk, an uncertain lifetime, and insurance. International Economic Review, 10 (3), 443–466.Google Scholar
Huang, H., Milevski, M.A. and Salisbury, T.S. (2012) Optimal retirement consumption with a stochastic force of mortality. Insurance: Mathematics and Economics, 51 (2), 282–291.Google Scholar
Kimball, M.S., Sahm, C.R. and Shapiro, M.D. (2008) Imputing risk tolerance from survey responses. Journal of the American Statistical Association 1; 103 (483), 1028–1038.Google Scholar
Koopmans, T.C. (1960) Stationary ordinal utility and impatience. Economectrica, 28 (2), 287–309.CrossRefGoogle Scholar
Kreps, D. (1988) Notes on the Theory of Choice. Underground Classics in Economics. Boulder and London: Westview Press.Google Scholar
Kreps, D. and Porteus, E. (1978) Temporal resolution of uncertainty and dynamic choice theory. Econometrica, 46, 185–200.Google Scholar
Lucas, R. (1978) Asset prices in an exchange economy. Econometrica, 46, 1429–1445.Google Scholar
Mehra, R. and Prescott, E.C. (1985) The equity premium: A puzzle. Journal of Monetary Economics, 22, 133–136.Google Scholar
Merton, R.C. (1969) Lifetime portfolio selection under uncertainty: The continuous-time case. The Review of Economics and Statistics, 51 (3), 247–57.CrossRefGoogle Scholar
Merton, R.C. (1971) Optimum consumption and portfolio rules in a continuous-time model. Journal of Economic Theory, 2 (4), 373–413.Google Scholar
Milevski, M. (1998) Optimal asset allocation towards the end of the life cycle: To annuitize or not to annuitize? Journal of Risk and Insurance, 65 (3), 401–426.Google Scholar
Mossin, J. (1968) Optimal multiperiod portfolio policies. Journal of Business, 41, 215–229.Google Scholar
Mossin, J. (1969) A note on uncertainty and preferences in a temporal context. The American Economic Review, 59 (1), 172–174.Google Scholar
Pliska, S. (1986) A stochastic calculus model of continuous trading: Optimal portfolios. Mathematics of Operations Research, 11, 371–382.CrossRefGoogle Scholar
Ramsey, F.P. (1928) A mathematical theory of saving. Economic Journal, December, 543–559.Google Scholar
Richard, S.F. (1975) Optimal consumption, portfolio and life insurance rules for an uncertain lived individual in a continuous time model. Journal of Financial Economics, 2, 187–203.Google Scholar
Rodden, J.A., Eskeland, G.S. and Litvack, J. (2003) Fiscal Decentralization and the Challenges of Hard Budget Constraints. Cambridge: The MIT Press, Massachusetts; London, England.Google Scholar
Samuelson, P. A. (1969) Lifetime portfolio selection by dynamic stochastic programming. Review of Economics and Statistics, 51 (3), 239–246.Google Scholar
Samuelson, P. A. (1989) The judgement on economic science on rational portfolio management: Indexing, timing, and long-horizon effects. Journal of Portfolio Management, 16 (1), 4–12.Google Scholar
Weil, P. (1989) The equity premium puzzle and the risk-free rate puzzle. Journal of Monetary Economics, 24, 501–521.Google Scholar
Yaari, M.E. (1965) Uncertain lifetime, life insurance, and the theory of the consumer. The Review of Economic Studies, 32 (2), 137–150.Google Scholar