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OPTIMAL INVESTMENT FOR A DEFINED-CONTRIBUTION PENSION SCHEME UNDER A REGIME SWITCHING MODEL

Published online by Cambridge University Press:  20 January 2015

An Chen  and
Łukasz Delong
An Chen
Affiliation:
Institute of Insurance Science, University of Ulm, Helmholtzstrasse 20, 89069 Ulm, Germany E-Mail: an.chen@uni-ulm.de
Łukasz Delong*
Affiliation:
Department of Probabilistic Methods, Institute of Econometrics, Warsaw School of Economics, Niepodleglosci 162, Warsaw 02-554, Poland
*
E-Mail: lukasz.delong@sgh.waw.pl
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Abstract

We study an asset allocation problem for a defined-contribution (DC) pension scheme in its accumulation phase. We assume that the amount contributed to the pension fund by a pension plan member is coupled with the salary income which fluctuates randomly over time and contains both a hedgeable and non-hedgeable risk component. We consider an economy in which macroeconomic risks are existent. We assume that the economy can be in one of I states (regimes) and switches randomly between those states. The state of the economy affects the dynamics of the tradeable risky asset and the contribution process (the salary income of a pension plan member). To model the switching behavior of the economy we use a counting process with stochastic intensities. We find the investment strategy which maximizes the expected exponential utility of the discounted excess wealth over a target payment, e.g. a target lifetime annuity.

Keywords

Exponential utility maximizationmacroeconomic riskscertainty equivalentbackward stochastic differential equations
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 45 , Issue 2 , May 2015 , pp. 397 - 419
Copyright
Copyright © ASTIN Bulletin 2015 

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References

Asprem, M. (1989) Stock prices, asset portfolios and macroeconomic variables in ten European countries. Journal of Banking and Finance, 13, 589–612.Google Scholar
Becherer, D. (2006) Bounded solutions to BSDE's with jumps for utility optimization and indifference hedging. The Annals of Applied Probability, 16, 2027–2054.CrossRefGoogle Scholar
Blake, D., Wright, D. and Zhang, Y.M. (2012) Target-driven investing: Optimal investment strategies in defined contribution pension plans under loss aversion. Journal of Economic Dynamics and Control, 37, 195–209.CrossRefGoogle Scholar
Bouchard, B. and Elie, R. (2008) Discrete time approximation of decoupled forward backward SDE with jumps. Stochastic Processes and their Applications, 118, 53–75.Google Scholar
Boulier, J.F., Huang, S.J. and Taillard, G. (2001) Optimal management under stochastic interest rates: The case of a protected defined contribution pension fund. Insurance: Mathematics and Economics, 28, 173–189.Google Scholar
Browne, S. (1995) Optimal investment policies for a firm with a random risk process: Exponential utility and minimizing the probability of ruin. Mathematics of Operations Research, 20 (4), 937–958.CrossRefGoogle Scholar
Cairns, A.J.G., Blake, D. and Dowd, K. (2006) Stochastic lifestyling: Optimal dynamic asset allocation for defined contribution pension plans. Journal of Economic Dynamics and Control, 30, 843–877.Google Scholar
Campbell, J.Y. (1987) Stock returns and the term structure. Journal of Financial Economics, 18, 373–399.CrossRefGoogle Scholar
Carmona, R. (2008) Indifference Pricing: Theory and Applications. Princeton: Princeton University Press.CrossRefGoogle Scholar
Crépey, S. (2011) About the pricing equation in finance. In Paris-Princeton Lectures in Mathematical Finance 2010 (ed., Carmona, R.A., Çinlar, E., Ekeland, I., Jouini, E., Scheinkman, J.A. and Touzi, N.), pp. 63–203. Berlin: Springer.Google Scholar
Delong, Ł. (2013) Backward Stochastic Differential Equations with Jumps and their Actuarial and Financial Applications. London: Springer.CrossRefGoogle Scholar
El Karoui, N., Peng, S. and Quenez, M.C. (1997) Backward stochastic differential equations in finance. Mathematical Finance, 7, 1–71.CrossRefGoogle Scholar
Elliott, R.J. and Siu, T.K., Badescu, A. (2011) On pricing and hedging options in regime-switching models with feedback effect. Journal of Economic Dynamics and Control, 35, 694–713.Google Scholar
Engle, R., Ghysels, E. and Sohn, B. (2008) On the economic sources of stock market volatility, Working paper.Google Scholar
Gao, J. (2008) Stochastic optimal control of dc pension funds. Insurance: Mathematics and Economics, 42, 1159–1164.Google Scholar
Hu, Y., Imkeller, P. and Müller, M. (2005) Utility maximization in incomplete markets. The Annals of Applied Probability, 15, 1691–1712.Google Scholar
Korn, R., Siu, T.K. and Zhang, A. (2011) Asset allocation for a DC pension fund under regime switching environment. European Actuarial Journal, 1, 361–377.Google Scholar
Longstaff, F. and Schwartz, E. (2001) Valuing american options by simulation: A simple least-squares approach. Review of Financial Studies, 14, 113–147.Google Scholar
Merton, R. (1969) Lifetime portfolio selection under uncertainty: The continuous-time case. Review of Economic Statistics, 51, 247–257.CrossRefGoogle Scholar
Merton, R. (1971) Optimum consumption and portfolio rules in a continuous-time model. Journal of Economic Theory, 3, 373–413.Google Scholar
Norberg, R. (2001) On Bonus and Bonus Prognoses in Life Insurance. Scandinavian Actuarial Journal, 2, 126–147.Google Scholar
Protter, P. (2004) Stochastic Integration and Differential Equations. Berlin: Springer.Google Scholar
Schwert, G. (1989) Why does stock market volatility change over time? Journal of Finance, 44, 1115–1153.Google Scholar