Computational Management Science

, Volume 6, Issue 3, pp 307–327 | Cite as

On multistage Stochastic Integer Programming for incorporating logical constraints in asset and liability management under uncertainty

  • Laureano F. Escudero
  • Araceli Garín
  • María Merino
  • Gloria Pérez
Original Paper

Abstract

We present a model for optimizing a mean-risk function of the terminal wealth for a fixed income asset portfolio restructuring with uncertainty in the interest rate path and the liabilities along a given time horizon. Some logical constraints are considered to be satisfied by the assets portfolio. Uncertainty is represented by a scenario tree and is dealt with by a multistage stochastic mixed 0-1 model with complete recourse. The problem is modelled as a splitting variable representation of the Deterministic Equivalent Model for the stochastic model, where the 0-1 variables and the continuous variables appear at any stage. A Branch-and-Fix Coordination approach for the multistage 0–1 program solving is proposed. Some computational experience is reported.

Keywords

Multistage scenario tree Assets and liabilities Stochastic Integer Programming Branch-and-Fix Coordination Mean-risk function 

AMS Subject Classification

90C15 90C11 90C06 

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References

  1. Ahn S, Escudero LF, Guignard-Spielberg M (1995) On modeling financial trading under interest rate uncertainty. In: Optimization in industry 3. Wiley, New York, pp 127–144Google Scholar
  2. Alonso-Ayuso A, Escudero LF, Ortuño MT (2003a) BFC, a Branch-and-Fix Coordination algorithmic framework for solving some types of stochastic pure and mixed 0-1 programs. Eur J Oper Res 151:503–519CrossRefGoogle Scholar
  3. Alonso-Ayuso A, Escudero LF, Garín A, Ortuño MT, Pérez G (2003b) An approach for strategic supply chain planning based on stochastic 0-1 programming. J Glob Optim 26:97–124CrossRefGoogle Scholar
  4. Ben-Dov Y, Mayre L, Pica V (1992) Mortgage valuation models at Prudential Securities. Interfaces 2:55–71CrossRefGoogle Scholar
  5. Benders JF (1962) Partitioning procedures for solving mixed variables programming problems. Numer Math 4:238–252CrossRefGoogle Scholar
  6. Birge JR (1985) Decomposition and partitioning methods for multi-stage stochastic linear programs. Oper Res 33:989–1007CrossRefGoogle Scholar
  7. Birge JR, Louveaux FV (1997) Introduction to stochastic programming. Springer, Berlin Heidelberg New YorkGoogle Scholar
  8. Black F, Derman E, Toy W (1990) A one factor model of interest rates and its application to treasury bond options. Financ Anal J Jan/Feb 33–39Google Scholar
  9. Dert CK (1998). A dynamic model for asset and liability management for defined benefit pension funds. In: Ziemba WT, Mulvey JM (eds). Worldwide asset and liability Modeling. Cambridge University Press, London, pp. 501–536Google Scholar
  10. Drijver SJ, Klein Haneveld WK, van der Vlerk MH (2003) Asset liability management modelling using multistage Mixed-Integer Stochastic Programming. In: Scherer B (ed) Asset and liability management tools, risk books. pp 309–324Google Scholar
  11. Escudero LF, Garín A, Merino M, Pérez G (2006) A two stage stochastic integer programming approach as a mixture of Branch-and-Fix Coordination and Benders Decomposition schemes. Ann Oper Res (in press)Google Scholar
  12. Fleten SE, Hoyland K, Wallace SW (2002) The performance of stochastic dynamic and fixed mix porfolio models. Eur J Oper Res 140:37–49CrossRefGoogle Scholar
  13. Gassmann HI (1990) MSLiP: a computer code for the multistage stochastic linear programming problem. Math Program 47:407–423CrossRefGoogle Scholar
  14. Klein Haneveld WK, van der Vlerk MH (1999) Stochastic integer programming: General models and algorithms. Ann Oper Res 85:39–57CrossRefGoogle Scholar
  15. Konno H, Yamamoto R (2005) Integer programming aproaches in mean-risk models. Comput Manage Sci 2:339–351CrossRefGoogle Scholar
  16. Kouwenberg R, Zenios SA (2006) Stochastic programming models for asset liability management. In: Zenios SA, Ziemba WT (eds) Handbook of asset and liability management, Vol. 1. North-Holland, Amsterdam, pp 253–303Google Scholar
  17. Laporte G, Louveaux FV (2002) An integer L-shaped algorithm for the capacitated vehicle routing problem with stochastic demands. Oper Res 50:415–423CrossRefGoogle Scholar
  18. Lulli G, Sen S (2004) A Branch-and-Price algorithm for multi-stage stochastic integer programming with application to stochastic batch-sizing problems. Manage Sci 50:786–796CrossRefGoogle Scholar
  19. Ntaimo L, Sen S (2005) The million variable “march” for stochastic combinatorial optimization. J Glob Optim 32:385–400CrossRefGoogle Scholar
  20. Ogryczak W, Ruszczynski A (1999) From stochastic dominace to mean-risk models: semi-deviations and risk measures. Eur J Oper Res 116:33–50CrossRefGoogle Scholar
  21. Rockafellar RT, Uryasev S (2000) Optimization of conditional value-at-risk. J Risk 2:21–41Google Scholar
  22. Rockafellar RT, Wets RJ-B (1991) Scenario and policy aggregation in optimisation under uncertainty. Math Oper Res 16:119–147CrossRefGoogle Scholar
  23. Römisch W, Schultz R (2001). Multi-stage stochastic integer programs: An introduction. In: Grötschel M, Krumke SO, Rambau J (eds). Online optimization of large scale systems. Springer, Berlin Heidelberg New York pp. 581–600Google Scholar
  24. Schultz R (2003) Stochastic programming with integer variables’. Math Program Ser B 97:285–309Google Scholar
  25. Schultz R, Tiedemann S (2004) Risk aversion via excess probabilities in stochastic programs with mixed-integer recourse. SIAM J Optim 14:115–138CrossRefGoogle Scholar
  26. Schultz R, Tiedemann S (2006) Conditional Value-at-Risk in stochastic programs with mixed integer recourse. Math Program Ser B 105:365–386CrossRefGoogle Scholar
  27. Sodhi MS (2005) LP modeling for asset-liability management: a survey of choices and simplifications. Oper Res 53:181–196CrossRefGoogle Scholar
  28. Zenios SA (1993) A model for portfolio management with mortgage-backed securities. Ann Oper Res 43:337–356CrossRefGoogle Scholar
  29. Ziemba WT (2003) The stochastic programming approach to asset, liability and wealth management. AIMR, CharlottevilleGoogle Scholar
  30. Ziemba WT, Mulvey JM ed. (1998) Worldwide asset and liability modeling. Cambridge University Press, LondonGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • Laureano F. Escudero
    • 1
  • Araceli Garín
    • 2
  • María Merino
    • 3
  • Gloria Pérez
    • 3
  1. 1.Centro de Investigación OperativaUniversidad Miguel HernándezElche (Alicante)Spain
  2. 2.Dpto. de Economía Aplicada IIIUniversidad del País VascoBilbao (Vizcaya)Spain
  3. 3.Dpto. de Matemática AplicadaEstadística e I.O, Universidad del País VascoLeioa (Vizcaya)Spain

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