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.
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References
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 127–144
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 151:503–519
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 26:97–124
Ben-Dov Y, Mayre L, Pica V (1992) Mortgage valuation models at Prudential Securities. Interfaces 2:55–71
Benders JF (1962) Partitioning procedures for solving mixed variables programming problems. Numer Math 4:238–252
Birge JR (1985) Decomposition and partitioning methods for multi-stage stochastic linear programs. Oper Res 33:989–1007
Birge JR, Louveaux FV (1997) Introduction to stochastic programming. Springer, Berlin Heidelberg New York
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 33–39
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. 501–536
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 309–324
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)
Fleten SE, Hoyland K, Wallace SW (2002) The performance of stochastic dynamic and fixed mix porfolio models. Eur J Oper Res 140:37–49
Gassmann HI (1990) MSLiP: a computer code for the multistage stochastic linear programming problem. Math Program 47:407–423
Klein Haneveld WK, van der Vlerk MH (1999) Stochastic integer programming: General models and algorithms. Ann Oper Res 85:39–57
Konno H, Yamamoto R (2005) Integer programming aproaches in mean-risk models. Comput Manage Sci 2:339–351
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 253–303
Laporte G, Louveaux FV (2002) An integer L-shaped algorithm for the capacitated vehicle routing problem with stochastic demands. Oper Res 50:415–423
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 50:786–796
Ntaimo L, Sen S (2005) The million variable “march” for stochastic combinatorial optimization. J Glob Optim 32:385–400
Ogryczak W, Ruszczynski A (1999) From stochastic dominace to mean-risk models: semi-deviations and risk measures. Eur J Oper Res 116:33–50
Rockafellar RT, Uryasev S (2000) Optimization of conditional value-at-risk. J Risk 2:21–41
Rockafellar RT, Wets RJ-B (1991) Scenario and policy aggregation in optimisation under uncertainty. Math Oper Res 16:119–147
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. 581–600
Schultz R (2003) Stochastic programming with integer variables’. Math Program Ser B 97:285–309
Schultz R, Tiedemann S (2004) Risk aversion via excess probabilities in stochastic programs with mixed-integer recourse. SIAM J Optim 14:115–138
Schultz R, Tiedemann S (2006) Conditional Value-at-Risk in stochastic programs with mixed integer recourse. Math Program Ser B 105:365–386
Sodhi MS (2005) LP modeling for asset-liability management: a survey of choices and simplifications. Oper Res 53:181–196
Zenios SA (1993) A model for portfolio management with mortgage-backed securities. Ann Oper Res 43:337–356
Ziemba WT (2003) The stochastic programming approach to asset, liability and wealth management. AIMR, Charlotteville
Ziemba WT, Mulvey JM ed. (1998) Worldwide asset and liability modeling. Cambridge University Press, London
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Escudero, L.F., Garín, A., Merino, M. et al. On multistage Stochastic Integer Programming for incorporating logical constraints in asset and liability management under uncertainty. Comput Manag Sci 6, 307–327 (2009). https://doi.org/10.1007/s10287-006-0035-7
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DOI: https://doi.org/10.1007/s10287-006-0035-7
Keywords
- Multistage scenario tree
- Assets and liabilities
- Stochastic Integer Programming
- Branch-and-Fix Coordination
- Mean-risk function