Abstract
In this paper we study possibilities for complexity reductions in large scale stochastic programming problems with specific reference to the asset liability management (ALM) problem for casualty insurers. We describe a dynamic, stochastic portfolio selection model, within which the casualty insurer maximizes a concave objective function, indicating that the company perceives itself as risk averse. In this context we examine the sensitivity of the solution to the quality and accuracy with which economic uncertainties are represented in the model. We demonstrate a solution method that combines two solution approaches: A truly stochastic, dynamic solution method that requires scenario aggregation, and a solution method based on ex ante decision rules, that allow for a greater number of scenarios. This dynamic/fix mix decision policy, which facilitates a huge number of outcomes, is then compared to a fully dynamic decision policy, requiring fewer outcomes. We present results from solving the model. Basically we find that the insurance company is likely to prefer accurate representation of uncertainties. In order to accomplish this, it will accept to calculate its current portfolio using parameterized decision rules.
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References
J. Birge, Comparison of static and dynamic asset allocation models, INFORMS National Meeting, Dallas, TX (October 28, 1997).
D.R. Carino, D.H. Myers and W.T. Ziemba, Concepts, technical issues, and uses of the Russell-Yasuda Kasai financial planning model, Operations Research 46(4) (1998).
D.R. Carino and W.T. Ziemba, Formulation of the Russell-Yasuda Kasai financial planning model, Operations Research 46(4) (1998).
D.R. Carino and A.L. Turner,Multiperiod asset allocation with derivative assets, in: World Wide Asset and Liability Modeling, eds. W.T. Ziemba and J.M. Mulvey (Cambridge University Press, 1997).
G. Consigli and M.A.H. Dempster, Dynamic stochastic programming for asset liability management, in: Proceedings of the APMOD95 Conference, London, Annals of Operations Research, forthcoming.
C. Dert, Asset liability management for pension funds, Ph.D. thesis, Erasmus University, Rotterdam, Netherlands (1995).
J. Dupacova, M. Bertocchi and V. Moriggia, Post-optimality for scenario based financial planning models with an application to bond portfolio management, in: World Wide Asset and Liability Modeling, eds. W.T. Ziemba and J.M. Mulvey (Cambridge University Press, 1997).
A.A. Gaivoronski and F. Stella, Nonstationary optimization approach for finding universal portfolios, Working Paper, Department of Industrial Economics and Technology Management, Norwegian University of Science and Technology, Trondheim, Norway (1998).
K. Høyland, S.E. Fleten and S. Wallace, The performance of stochastic dynamic and fixed mix portfolio models, Working paper, Department of Industrial Economics and Technology Management, Norwegian University of Science and Technology, Trondheim, Norway (1998).
K. Høyland and S. Wallace, Generating scenario trees for multistage problems, Working paper no 4/97, Department of Industrial Economics and Technology Management, Norwegian University of Science and Technology, Trondheim, Norway (1998), forthcoming in Management Science.
K. Høyland and S. Wallace, Analyzing legal regulations in the Norwegian life insurance business using a multistage asset liability management model, Working paper no 5/97, Department of Industrial Economics and Technology Management, Norwegian University of Science and Technology, Trondheim, Norway (1998).
P. Kall and S. Wallace, Stochastic Programming (Wiley, 1994).
A.J. King, Asymmetric risk measures and tracking models for portfolio optimization under uncertainty, Ann. Oper. Res. 45 (1993) 165–177.
P. Klassen, Financial asset-pricing theory and stochastic programming models for asset/liability management: a synthesis, Management Science 44 (1998) 31–48.
R. Kouwenberg, A stochastic programming model for asset liability management for pension funds, Erasmus Centre for Financial Research (ECFR), Report 9801, Erasmus University Rotterdam (1998).
M.I. Kusy and W.T. Ziemba, A bank asset and liability model, Operations Research 3 (1986) 356–376.
J.M. Mulvey and H. Vladimirou, Stochastic network planning for financial planning problems, Management Science 38 (1992) 1642–1664.
J.M. Mulvey and H. Vladimirou, Applying the progressive hedging algorithm to stochastic generalized networks, Annals of Operations Research 31 (1991) 399–424.
R.T. Rokafellar and R.J.-B.Wets, Scenarios and policy aggregation in optimization under uncertainty, Mathematics of Operations Research 16 (1991) 119–147.
C. Vassiadou-Zeniou and S.A. Zenios, Robust optimization models for managing callable bond portfolios, European Journal of Operational Research (1996) 264–273.
S.A. Zenios, M.R. Holmer, R. McKendall and C. Vassiadou-Zeniou, Dynamic models for fixed income portfolio management, Working Paper, Department of Public and Business Administration, University of Cyprus, Nicosia, Cyprus (1997).
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Gaivoronski, A.A., de Lange, P.E. An Asset Liability Management Model for Casualty Insurers: Complexity Reduction vs. Parameterized Decision Rules. Annals of Operations Research 99, 227–250 (2000). https://doi.org/10.1023/A:1019223800849
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DOI: https://doi.org/10.1023/A:1019223800849