Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-06T09:04:33.601Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimal investment strategy for a DC pension fund plan in a finite horizon time: an optimal stochastic control approach

Published online by Cambridge University Press:  18 February 2022

Saman Vahabi  and
Amir T. Payandeh Najafabadi Open the ORCID record for Amir T. Payandeh Najafabadi [Opens in a new window]
Saman Vahabi
Affiliation:
Department of Actuarial Science, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran
Amir T. Payandeh Najafabadi*
Affiliation:
Department of Actuarial Science, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran
*
*Corresponding author. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper obtains an optimal strategy in a finite horizon time for a portfolio of a defined contribution (DC) pension fund for an investor with the CRRA utility function. It employs the optimal stochastic control method in a financial market with two different asset markets, one risk-free and another one risky asset in which its jump follows either by a finite or infinite activity Lévy process. Sensitivity of jump parameters in an uncertainty financial market has been studied.

Keywords

Optimal strategyPension plansPension fundFinite/Infinite activity Lévy processes
Type
Original Research Paper
Information
Annals of Actuarial Science , Volume 16 , Issue 2 , July 2022 , pp. 367 - 383
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Institute and Faculty of Actuaries

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

Aït-Sahalia, Y., Cacho-Diaz, J. & Hurd, T.R. (2009). Portfolio choice with jumps: a closed-form solution. Annals of Applied Probability, 19(2), 556–584.CrossRefGoogle Scholar
Applebaum, D. (2009). Lévy Processes and Stochastic Calculus. Cambridge University Press, New York.CrossRefGoogle Scholar
Campbell, J.Y., Champbell, J.J., Campbell, J.W., Lo, A.W., Lo, A.W. & MacKinlay, A.C. (1997). The Econometrics of Financial Markets. princeton University Press.CrossRefGoogle Scholar
Choulli, T. & Hurd, T.R. (2001). The role of Hellinger processes in mathematical finance. Entropy, 3(3), 150–161.CrossRefGoogle Scholar
Cont, R. & Tankov, P. (2004). Financial Modelling with Jump Processes. Chapman and Hall/CRC.Google Scholar
Cont, R. & Tankov, P. (2009). Constant proportion portfolio insurance in the presence of jumps in asset prices. Mathematical Finance: An International Journal of Mathematics, Statistics and Financial Economics, 19(3), 379–401.CrossRefGoogle Scholar
Cox, J.C. & Huang, C.F. (1989). Optimal consumption and portfolio policies when asset prices follow a diffusion process. Journal of economic theory, 49(1), 33–83.CrossRefGoogle Scholar
Deelstra, G., Grasselli, M. & Koehl, P.F. (2004). Optimal design of the guarantee for defined contribution funds. Journal of Economic Dynamics and Control, 28(11), 2239–2260.CrossRefGoogle Scholar
Devroye, L. (2006). Nonuniform random variate generation. In Handbooks in Operations Research and Management Science (pp. 83–121), vol. 13.CrossRefGoogle Scholar
Dong, Y. & Zheng, H. (2019). Optimal investment of DC pension plan under short-selling constraints and portfolio insurance. Insurance: Mathematics and Economics, 85, 47–59.Google Scholar
Dong, Y. & Zheng, H. (2020). Optimal investment with S-shaped utility and trading and Value at Risk constraints: an application to defined contribution pension plan. European Journal of Operational Research, 281(2), 341–356.CrossRefGoogle Scholar
Emmer, S. & Klüppelberg, C. (2004). Optimal portfolios when stock prices follow an exponential Lévy process. Finance and Stochastics, 8(1), 17–44.CrossRefGoogle Scholar
Gao, J. (2008). Stochastic optimal control of DC pension funds. Insurance: Mathematics and Economics, 42(3), 1159–1164.Google Scholar
Gradshteyn, I.S. & Ryzhik, I.M. (2014). Table of Integrals, Series, and Products. Academic Press.Google Scholar
Iscanoglu-Cekic, A. (2016). An optimal Turkish private pension plan with a guarantee feature. Risks, 4(3), 19.CrossRefGoogle 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.CrossRefGoogle Scholar
Kallsen, J. (2000). Optimal portfolios for exponential Lévy processes. Mathematical Methods of Operations Research, 51(3), 357–374.CrossRefGoogle Scholar
Korn, R. (1997). Optimal Portfolios: Stochastic Models for Optimal Investment and Risk Management in Continuous Time. World Scientific.CrossRefGoogle Scholar
Kou, S.G. (2002). A jump-diffusion model for option pricing. Management Science, 48(8), 1086–1101.CrossRefGoogle Scholar
Kou, S.G. & Wang, H. (2004). Option pricing under a double exponential jump diffusion model. Management Science, 50(9), 1178–1192.CrossRefGoogle Scholar
Lamberton, D. & Lapeyre, B. (2007). Introduction to Stochastic Calculus Applied to Finance. CRC Press.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.CrossRefGoogle Scholar
Liang, Z. & Ma, M. (2015). Optimal dynamic asset allocation of pension fund in mortality and salary risks framework. Insurance: Mathematics and Economics, 64, 151–161.Google Scholar
Liu, J., Longstaff, F.A. & Pan, J. (2003). Dynamic asset allocation with event risk. The Journal of Finance, 58(1), 231–259.CrossRefGoogle Scholar
Madan, D.B. & Seneta, E. (1990). The variance gamma (VG) model for share market returns. Journal of Business, 63(4), 511–524.CrossRefGoogle Scholar
Madan, D. (2001). Financial Modeling with Discontinuous Price Processes. Lévy Processes-Theory and Applications. Birkhauser, Boston.Google Scholar
Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1), 77–91.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.CrossRefGoogle Scholar
Merton, R.C. (1975). Optimum consumption and portfolio rules in a continuous-time model. In Stochastic Optimization Models in Finance. Academic Press.Google Scholar
Merton, R.C. (1976). Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics,3(1–2), 125–144.CrossRefGoogle Scholar
Øksendal, B. (2013). Stochastic Differential Equations: An Introduction with Applications. Springer Science and Business Media.Google Scholar
Øksendal, B.K. & Sulem, A. (2005). Applied Stochastic Control of Jump Diffusions, vol. 498. Springer, Berlin.Google Scholar
Pasin, L. & Vargiolu, T. (2010). Optimal portfolio for CRRA utility functions when risky assets are exponential additive processes. Economic Notes, 39(1–2), 65–90.CrossRefGoogle Scholar
Xu, W. & Gao, J. (2020). An optimal portfolio problem of DC pension with input-delay and jump-diffusion process. Mathematical Problems in Engineering, 2020, 1–9.Google Scholar
Yao, H., Chen, P., Zhang, M. & Li, X. (2020). Dynamic discrete-time portfolio selection for defined contribution pension funds with inflation risk. Journal of Industrial and Management Optimization, 13(5), 1–30.Google Scholar