Zhang, Aihua and Korn, Ralf and Ewald, Christian-Oliver (2007): Optimal management and inflation protection for defined contribution pension plans.
Download (1189Kb) | Preview
Due to the increasing risk of inflation and diminishing pension benefits, insurance companies have started selling in°ation-linked products. Selling such products the insurance company takes over some or all of the inflation risk from their customers. On the other side financial derivatives which are linked to inflation such as inflation linked bonds are traded on financial markets and appear to be of increasing popularity. The insurance company can use these products to hedge its own inflation risk. In this article we study how to optimally manage a pension fund taking positions in a money market account, a stock and an inflation linked bond, while financing investments through a continuous stochastic income stream such as the plan member's contributions. We use the martingale method in order to compute an analytic expression for the optimal strategy and express it in terms of observable market variables.
|Item Type:||MPRA Paper|
|Institution:||University of St.Andrews, School of Economics and Finance|
|Original Title:||Optimal management and inflation protection for defined contribution pension plans|
|Keywords:||Pension mathematics; in°ation; long-term investment; stochastic optimal control; martingale method|
|Subjects:||E - Macroeconomics and Monetary Economics > E4 - Money and Interest Rates > E44 - Financial Markets and the Macroeconomy
G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing; Trading volume; Bond Interest Rates
C - Mathematical and Quantitative Methods > C6 - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C61 - Optimization Techniques; Programming Models; Dynamic Analysis
|Depositing User:||Christian-Oliver Ewald|
|Date Deposited:||22. May 2007|
|Last Modified:||12. Feb 2013 22:06|
 Battocchio, P., Menoncin, F., (2002) Optimal pension management under stochastic interest rates, wages and in°ation Discussion paper, IRES.
 Beletski, T., Korn, R., (2006) Optimal investment with in°ation-linked products. Advances in Risk Management (Ed. G.N. Gregoriou), Palgrave-Mac Millan, 170- 190.
 Blake, D., Cairns, A.J.G, Dowd, K. (2001) Pension metrics: stochastic pension plan design and value-at-risk during the accumulation phase. Insurance: Mathe- matics and Economics 29, 187-215.
 Black, F. Scholes, M. The pricing of options and corporate liabilities. Journal of Political Economy 81, 637-659. (1973)
 Cairns, A.J.G. (2000) Some notes on the dynamics and optimal control of stochastic pension fund models in continuous time. ASTIN Bulletin 30, 19-55.
 Cairns, A.J.G, Blake, D., Dowd, K. (2004) Stochastic life styling: optimal dynamics asset allocation for de¯ned contribution pension plans. J. Economics and Control 30(5), 843-877.
 Deelstra, G., Grasselli, M., Koehl, P.F. (2000) Optimal investment strategies in a CIR framework. J. Appl. Prob. 37, 936-946.
 Deelstra, G., Grasselli, M., Koehl, P.F. (2002) Optimal design of the guarantee for de¯ned contribution funds. Preprint.
 Fisher, I. (1930) The Theory of Interest. MacMillan Press Ltd. London, Bas- ingstoke
 Karatzas, I., Lehoczky, J.P., Shreve, S.E., Xu, G.L (1991) Martingale and duality for utility maximization in an incomplete market. SIAM J. Control and Optimization 29, 702-730.
 Korn, R., Korn, E., (2000) Option Pricing and portfolio optimization. Graduate studies in mathematics, Vol 31, American Mathematical Society.
 Korn, R. Kruse, S. (2004) Einfache Verfahren zur Bewertung von in°ationsgekop- pelten Finanzprodukten. Bltter der DGVFM, XXVI(3), 351-67.