Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-25T11:07:32.719Z Has data issue: false hasContentIssue false
  • English
  • Français

ON INTEGRATED CHANCE CONSTRAINTS IN ALM FOR PENSION FUNDS

Published online by Cambridge University Press:  19 February 2018

Youssouf A. F. Toukourou  and
François Dufresne
Youssouf A. F. Toukourou*
Affiliation:
Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne UNIL-Dorigny, CH-1015 Lausanne, Switzerland
François Dufresne
Affiliation:
Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne UNIL-Dorigny, CH-1015 Lausanne, Switzerland
*
E-Mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We discuss the role of integrated chance constraints (ICC) as quantitative risk constraints in asset and liability management (ALM) for pension funds. We define two types of ICC: the one period integrated chance constraint (OICC) and the multiperiod integrated chance constraint (MICC). As their names suggest, the OICC covers only one period, whereas several periods are taken into account with the MICC. A multistage stochastic linear programming model is therefore developed for this purpose and a special mention is paid to the modeling of the MICC. Based on a numerical example, we first analyze the effects of the OICC and the MICC on the optimal decisions (asset allocation and contribution rate) of a pension fund. By definition, the MICC is more restrictive and safer compared to the OICC. Second, we quantify this MICC safety increase. The results show that although the optimal decisions from the OICC and the MICC differ, the total costs are very close, showing that the MICC is definitely a better approach since it is more prudent.

Keywords

Pension fundsmodelingasset liability managementmultistage stochastic programminglinear programmingintegrated chance constraint
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 48 , Issue 2 , May 2018 , pp. 571 - 609
Copyright
Copyright © Astin Bulletin 2018 

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

Ahlgrim, K.C., Dárcy, S.P. and Gorvett, R.W. (2005) Modeling financial scenarios: A framework for the actuarial profession. In Proceedings of the Casualty Actuarial Society, volume 92, pp. 177–238. Casualty Actuarial Society Arlington, VA.Google Scholar
Ahmed, S. and Shapiro, A. (2008) Solving chance-constrained stochastic programs via sampling and integer programming. In 2008 Tutorials in Operations Research: State-of-the-Art Decision-Making Tools in the Information-Intensive Age (eds. Chen, Z.-L. and Raghavan, S.), pp. 261–269. Catonsville, MD: INFORMS.Google Scholar
Aro, H. and Pennanen, T. (2013) Liability-driven investment in longevity risk management. In Optimal Financial Decision Making under Uncertainty (eds. Consigli, G., Kuhn, D. and Brandimarte, P.), pp. 121–136. Cham, Switzerland: Springer International Publishing.Google Scholar
Artzner, P., Delbaen, F., Eber, J.-M. and Heath, D. (1999) Coherent measures of risk. Mathematical Finance, 9 (3), 203–228.Google Scholar
Birge, J.R. and Louveaux, F.V. (2011) Introduction to Stochastic Programming. New York: Springer-Verlag.CrossRefGoogle Scholar
Bogentoft, E., Romeijn, H.E. and Uryasev, S. (2001) Asset/liability management for pension funds using CVaR constraints. Journal of Risk Finance, 3 (1), 57–71.Google Scholar
Carino, D.R., Kent, T., Myers, D.H., Stacy, C., Sylvanus, M., Turner, A.L., Watanabe, K. and Ziemba, W.T. (1994) The Russell-Yasuda Kasai model: An asset/liability model for a Japanese insurance company using multistage stochastic programming. Interfaces, 24 (1), 29–49.Google Scholar
Charnes, A., Cooper, W.W. and Symonds, G.H. (1958) Cost horizons and certainty equivalents: An approach to stochastic programming of heating oil. Management Science, 4 (3), 235–263.Google Scholar
Consigli, G. and Dempster, M.A.H. (1998) Dynamic stochastic programming for asset-liability management. Annals of Operations Research, 81, 131–162.CrossRefGoogle Scholar
Dert, C. (1995) Asset Liability Management for Pension Funds: A Multistage Chance Constrained Programming Approach. Erasmus Universiteit Rotterdam.Google Scholar
Drijver, S.J. (2005) Asset Liability Management for Pension Funds Using Multistage Mixed-Integer Stochastic Programming. Groningen, The Netherlands: University of Groningen.Google Scholar
Elton, E.J. and Gruber, M.J. (1992) Optimal investment strategies with investor liabilities. Journal of Banking & Finance, 16 (5), 869–890.Google Scholar
Faleh, A. (2011) Un modèle de programmation stochastique pour l'allocation stratégique d'actifs d'un régime de retraite partiellement provisionné. Working Paper. Available at: https://hal.archives-ouvertes.fr/hal-00561965/document.Google Scholar
Fama, E.F. (1970) Multiperiod consumption-investment decisions. The American Economic Review, 60, 163–174.Google Scholar
Fonseca, R., Michaud, P.-C. and Sopraseuth, T. (2007) Richesse, contrainte de liquidité et coût de création déntreprise. Technical report, Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne.Google Scholar
Geyer, A. and Ziemba, W.T. (2008) The innovest Austrian pension fund financial planning model InnoALM. Operations Research, 56 (4), 797–810.CrossRefGoogle Scholar
Gottlieb, L. C. and Whiston, B. A. (2005) Morneau Sobeco Handbook of Canadian Pension and Benefit Plans, 13th edition. Toronto: CCH Canadian Limited.Google Scholar
Hakansson, N.H. (1970) Optimal investment and consumption strategies under risk for a class of utility functions. Econometrica: Journal of the Econometric Society, 587–607.CrossRefGoogle Scholar
Hakansson, N.H. (1974) Convergence to isoelastic utility and policy in multiperiod portfolio choice. Journal of Financial Economics, 1 (3), 201–224.Google Scholar
Haneveld, W.K.K. (1986) Duality in Stochastic Linear and Dynamic Programming, Lecture Notes in Economics and Mathematical Systems, volume 274. Berlin: Springer-Verlag.Google Scholar
Haneveld, W.K.K. and Van Der Vlerk, M.H. (2002) Integrated Chance Constraints: Reduced Forms and An Algorithm. Groningen, The Netherlands: University of Groningen.Google Scholar
Haneveld, W.K.K., Streutker, M.H. and Van Der Vlerk, M.H. (2010) An alm model for pension funds using integrated chance constraints. Annals of Operations Research, 177 (1), 47–62.Google Scholar
Hiller, R.S. and Schaack, C. (1990) A classification of structured bond portfolio modeling techniques. The Journal of Portfolio Management, 17 (1), 37–48.CrossRefGoogle Scholar
Hilli, P., Koivu, M., Pennanen, T. and Ranne, A. (2007) A stochastic programming model for asset liability management of a Finnish pension company. Annals of Operations Research, 152 (1), 115–139.Google Scholar
Kall, P. and Mayer, J. (2011) Stochastic Linear Programming: Models, Theory, and Computation. Berlin: Springer-Verlag.Google Scholar
Keel, A. and Müller, H.H. (1995) Efficient portfolios in the asset liability context. ASTIN Bulletin, 25 (01), 33–48.Google Scholar
Koopmans, K.C. (1942) The Risk of Interest Fluctuations in Life Insurance Companies. Philadelphia: Penn Mutual Life Insurance Company.Google Scholar
Kouwenberg, R. (2001) Scenario generation and stochastic programming models for asset liability management. European Journal of Operational Research, 134 (2), 279–292.Google Scholar
Kusy, M.I. and Ziemba, W.T. (1986) A bank asset and liability management model. Operations Research, 34 (3), 356–376.CrossRefGoogle Scholar
Leibowitz, M.L. and Henriksson, R.D. (1988) Portfolio optimization within a surplus framework. Financial Analysts Journal, 44 (2), 43–51.Google Scholar
Leibowitz, M.L., Kogelman, S. and Bader, L.N. (1992) Asset performance and surplus control: A dual-shortfall approach. The Journal of Portfolio Management, 18 (2), 28–37.Google Scholar
Luedtke, J. (2013) A branch-and-cut decomposition algorithm for solving chance-constrained mathematical programs with finite support. Mathematical Programming, 146 (1–2), 1–26.Google Scholar
Luedtke, J., Ahmed, S. and Nemhauser, G.L. (2010) An integer programming approach for linear programs with probabilistic constraints. Mathematical Programming, 122 (2), 247–272.Google Scholar
Markowitz, H. (1952) Harry Markowitz. Portfolio selection, 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.Google Scholar
Møller, T. and Steffensen, M. (2007) Market-Valuation Methods in Life and Pension Insurance. Cambridge: Cambridge University Press.Google Scholar
Nemirovski, A. and Shapiro, A. (2006) Convex approximations of chance constrained programs. SIAM Journal on Optimization, 17 (4), 969–996.Google Scholar
Pflug, G.Ch., Swietanowski, A. and Paeug, G.Ch. (1998) Dynamic asset allocation under uncertainty for pension fund management. Control and Cybernetics, 28 (4), 755–777.Google Scholar
Prékopa, A. (1998) Programming under probabilistic constraint with discrete random variable. In New Trends in Mathematical Programming (eds. Giannessi, F., Komlósi, S. and Rapcsák, T.), pp. 235–255. Dordrecht: Springer Science+Business Media.Google Scholar
Raike, W.M. (1970) Dissection methods for solutions in chance constrained programming problems under discrete distributions. Management Science, 16 (11), 708–715.Google Scholar
Redington, F.M. (1952) Review of the principles of life-office valuations. Journal of the Institute of Actuaries, 78 (3), 286–340.Google Scholar
Rockafellar, R.T. and Uryasev, S. (2002) Conditional value-at-risk for general loss distributions. Journal of Banking & Finance, 26 (7), 1443–1471.Google Scholar
Ruszczyński, A. (2002) Probabilistic programming with discrete distributions and precedence constrained knapsack polyhedra. Mathematical Programming, 93 (2), 195–215.Google Scholar
Shapiro, A., Dentcheva, D. and Ruszczyński, A. (2009) Lectures on Stochastic Programming: Modeling and Theory, volume 9. Philadelphia: Society for Industrial and Applied Mathematics and the Mathematical Planning Society.Google Scholar
Sharpe, W.F. and Tint, L.G. (1990) Liabilities-a new approach. The Journal of Portfolio Management, 16 (2), 5–10.Google Scholar
Tanner, M.W. and Ntaimo, L. (2010) IIS branch-and-cut for joint chance-constrained stochastic programs and application to optimal vaccine allocation. European Journal of Operational Research, 207 (1), 290–296.Google Scholar
Watson, Towers. (2003) Global Pensions Asset Study. Available at: https://towerswatson.com/en/Insights/IC-Types/Survey-Research-Results/2013/01/Global-Pensions-Asset-Study-2013.Google Scholar
van der Vlerk, M.H., Haneveld, W.K.K. and Streutker, M.H. (2003) Integrated Chance Constraints in an ALM Model for Pension Funds. Berlin: Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik.Google Scholar
Wilkie, A.D. (1995) More on a stochastic asset model for actuarial use. British Actuarial Journal, 1 (05), 777–964.Google Scholar
Zenios, S.A. (2006) Practical Financial Optimization: Decision Making for Financial Engineers. Oxford: Blackwell Publishing.Google Scholar
Ziemba, W.T. and Mulvey, J.M. (1998) Worldwide Asset and Liability Modeling, volume 10. Cambridge: Cambridge University Press.Google Scholar