A Defined Benefit Pension Fund ALM Model through Multistage Stochastic Programming

Document Type : Original Article

Authors

1 Department of Management, Economics and Quantitative Methods University of Bergamo, Italy

2 Department of Management, Economics and Quantitative Methods University of Bergamo, Italy (Corresponding author)

Abstract

We consider an asset-liability management (ALM) problem for a defined benefit pension fund (PF). The PF manager is assumed to follow a maximal fund valuation problem facing an extended set of risk factors:  due to the longevity of the    PF members, the inflation affecting salaries in real terms and future incomes, interest rates and market factors affecting jointly the PF liability and asset portfolio. The problem is formulated as a stochastic programming problem in discrete time and with a discrete set of relevant future economic and demographic scenarios. In real world applications, this class of decision problems under uncertainty leads to very large scale and complex management problems, due to pending regulatory constraints and the need to preserve the PF funding conditions. Dynamic stochastic programming is shown under such conditions to provide a natural and effective mathematical and numerical approach.

Keywords

References

1)     Beraldi P., De Simone F., Violi A. (2010). Generating scenario trees: a parallel integrated simulation optimization approach, Comput. Appl. Math., 233, pp. 2322-233.
2)     Beraldi, P., Consigli, G., De Simone, F., Iaquinta, G. and Violi, A. (2011). Hedging market and credit risk in corporate bond portfolios, In Handbook on Stochastic Optimization Methods in Finance and Energy, Fred Hillier International Series in Operations Research and Management Science, edited by M. Bertocchi, G. Consigli and M. Dempster, Chapter 4, pp. 73-98 (Springer: New York).
3)     Bertocchi M., Dupaˆcová J., Moriggia V. (2007). Bond portfolio management via stochastic programming, In Handbook of asset and liability management, vol. 1, Theory and methodology, ed. S. A. Zenios and W. T. Ziemba, 305-336.
4)     Castro J. (2009). A stochastic programming approach to cash management in banking, European Journal of Operational Research,192, 963-974.
5)     Chiralaksanakul A., Morton D. P. (2004). Assessing policy quality in multi-stage stochastic programming, Stochastic Programming E-Print Series 12.
6)     Consigli, G., Dempster, M.A.H. (1998). Dynamic stochastic programming for asset-liability management, Ann. Oper. Res. 81, 131-161.
7)     Consigli G., di Tria M., Gaffo M., Iaquinta G., Moriggia V., Uristani A. (2011). Dynamic Portfolio Management for Property and Casualty Insurance. In Handbook on Stochastic Optimization Methods in Finance and Energy, Fred Hillier International Series in Operations Research and Management Science, edited by M. Bertocchi, G. Consigli and M. Dempster, Chapter 5, pp. 99-124, Springer:  New York.
8)     Consiglio A., Cocco F., Zenios S.A. (2008). Asset and liability modelling for participating policies with guarantees, European Journal of Operational Research 186, 380-404.
9)     Consiglio A., Carollo A., Zenios S.A. (2016). A parsimonious model for generating arbitrage-free scenario trees, Quantitative Finance, 01, Vol.16(2), p.201-212.
10)  Dempster M. A. H., Germano M., Medova E. A., and Villaverde M. (2003). Global asset liability management, British Actuarial Journal, 9 (1):137195 Part c.
11)  Dempster M.A.H., Germano M., Medova E., Murphy J., Ryan D., Sandrini F. (2009). Risk Profiling Defined Benefit Pension Schemes, The Journal of Portfolio Management, Vol.35(4), pp.76-93.
12)  Dempster M. A. H., Medova E. A., Yong Y. S. (2011). Comparison of Sampling Methods for Dynamics Stochastic Programming, Stochastic Optimization Methods in Finance and Energy, Ch. 16, Springer.
13)  Dempster M. A. H., Medova E. A., Rietbergen M. I., Sandrini F., Scrowston M. (2011). Designed Minimum Guaranteed Return Funds, Stochastic Optimization Methods in Finance and Energy, Ch. 2, Springer.
14)  Dondi G. and Herzog F. (2007). Dynamic Asset and Liabilities Management for Swiss Pension Funds, Handbook of Asset and Liability Management Volume 2, Ch.20.
15)  Dupaˆcová J., Consigli G., Wallace S. W. (2000). Scenarios for multistage stochastic programs, Annals of Operations Research.
16)  Dupaˆcová, J., Bertocchi, M. (2001). From data to model and back to data: A bond portfolio management problem, European Journal of Operational Research 134, 261-278.
17)  Dupaˆcová J., Polìvka J. (2009). Asset-liability-management for Czech pension funds using stochastic programming, Annals of Operations Research, Vol.165(1), pp.5-28.
18)  Geyer A., Ziemba W. T. (2008). The Innovest Austrian Pension Fund Financial Planning Model InnoALM, Operations Research, Vol.56(4), p.797- 810.
19)  Geyer A., Hanke M., Weissensteiner A. (2014). No-arbitrage bounds for financial scenarios, European Journal of Operational Research, 236(2), 657-663.
20)  Geyer A., Hanke M., Weissensteiner A. (2014). No-Arbitrage ROM simulation, Journal of Economic Dynamics & Control, 45, 66-79.
21)  Glosten L., Jagannathan R., Runkle D. (1993). Relationship between the expected value and volatility of the nominal excess returns on stocks, Journal of Finance, 48, 1779-1802.
22)  Gülpinar N., Rustem B., Settergren R. (2004). Simulation and optimization approaches to scenario tree generation, Journal of Economic Dynamics and Control, Vol.28(7), pp.1291-1315.
23)  Heitsch H., Romisch W. (2005). Generation of multivariate scenario trees to model stochasticity in power management, IEEE St. Petersburg Power Tech.
24)  Hochreiter R., Pflug G. (2007). Financial scenario generation for stochastic multi-stage decision processes as facility location problems, Annals of Operations Research
International Journal of Finance & Managerial Accounting
Volume 2, Issue 7
October 2017
Pages 1-10

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