Skip to main content

Stochastic Optimization in Asset & Liability Management: A Model for Non-Maturing Accounts

  • Chapter
Probabilistic Constrained Optimization

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 49))

Abstract

A multistage stochastic optimization model for the management of non-maturing account positions like savings deposits and variable-rate mortgages is introduced which takes the risks induced by uncertain future interest rates and customer behavior into account. Stochastic factors are discretized using the barycentric approximation technique. This generates two scenario trees whose associated deterministic equivalent programs provide exact upper and lower bounds to the original problem. Practical experience from the application in a major Swiss bank is reported.

Research for this paper was supported by the Swiss National Science Foundation, Grant No. 21-39′575.93.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J.R. Birge and R.J.-B. Wets. Designing approximation schemes for stochastic optimization problems, in particular for stochastic programs with recourse. Mathematical Programming Study, 27:54–102, 1986.

    Article  MathSciNet  MATH  Google Scholar 

  2. J.R. Birge, C.J. Donohue, D.F. Holmes, and O.G. Svintsitski. A parallel implementation of the nested decomposition algorithm for multistage stochastic linear programs. Mathematical Programming, 75:327–352, 1995.

    MathSciNet  Google Scholar 

  3. M. Britton-Jones. The sampling error in estimates of mean-variance efficient portfolio weights. Journal of Finance, 54:655–671, 1999.

    Article  Google Scholar 

  4. D.R. Cariho, T. Kent, D.H. Myers, C. Stacy, M. Sylvanus, A.L. Turner, K. Watanabe, and W.T. Ziemba. The Russell-Yasuda Kasai model: An asset/liability model for a Japanese insurance company using multistage stochastic programming. Interfaces, 24:29–49, 1994.

    Article  Google Scholar 

  5. D.R. Carifio, D.H. Myers, and W.T. Ziemba. Conceps, technical issues, and uses of the Russell-Yasuda Kasai financial planning model. Operations Research, 46:450–462, 1998.

    Article  MathSciNet  Google Scholar 

  6. D.R. Carifio and W.T. Ziemba. Formulation of the Russell-Yasuda Kasai financial planning model. Operations Research, 46:433–449, 1998.

    Article  MathSciNet  Google Scholar 

  7. Z. Chen, G. Consigli, M.A.H. Dempster, and N. Hicks-Pedrön. Towards sequential sampling algorithms for dynamic portfolio management. In: C. Zopounidis (ed.), Operational Tools in the Management of Financial Risks, pp. 197–211. Kluwer, 1998.

    Chapter  Google Scholar 

  8. V.K. Chopra and W.T. Ziemba. The effect of errors in means, variances, and covariances on optimal portfolio choice. Journal of Portfolio Management, 20:6–11, 1993.

    Article  Google Scholar 

  9. G. Consigli and M.A.H. Dempster. Solving dynamic portfolio problems using stochastic programming. Zeitschrift für Angewandte Mathematik und Mechanik (Supplement), 77: S535–S536, 1997.

    MATH  Google Scholar 

  10. G.B. Dantzig and G. Infanger. Large-scale stochastic linear programs: Importance sampling and Benders decomposition. Technical Report SOL 91–4, Stanford University, 1991.

    Google Scholar 

  11. G.B. Dantzig and G. Infanger. Multi-stage stochastic linear programs for portfolio optimization. Annals of Operations Research, 45:59–76, 1993.

    Article  MathSciNet  MATH  Google Scholar 

  12. R. Dembo. Scenario optimization. Annals of Operations Research, 30:63–80, 1991.

    Article  MathSciNet  MATH  Google Scholar 

  13. M.A.H. Dempster. The expected value of perfect information in the optimal evolution of stochastic problems. In: M. Arato, D. Vermes, and A.V. Balakrishnan (eds.), Stochastic Differential Systems, pp. 25–40. Springer, 1981.

    Chapter  Google Scholar 

  14. C.L. Dert. Asset liability management for pension funds: A multistage chance constraint programming approach. Phd thesis, Erasmus University, Rotterdam, 1995.

    Google Scholar 

  15. J. Dupacovâ. Stochastic programming models in banking. Working paper, HAS A, Laxenburg, 1991.

    Google Scholar 

  16. J. Dupacovâ. Postoptimality for multistage stochastic linear programs. Annals of Operations Research, 56:65–78, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  17. J. Dupacovâ. Scenario-based stochastic programs: Resistance with respect to sample. Annals of Operations Research, 64:21–38, 1996.

    Article  MathSciNet  MATH  Google Scholar 

  18. J. Dupacovâ, M. Bertocchi, and V. Moriggia. Postoptimality for scenario based financial planning models with an application to bond portfolio management. In: W.T. Ziemba and J.M. Mulvey (eds.), World Wide Asset and Liability Modeling, pp. 263–285. Cambridge University Press, Cambridge, 1998.

    Google Scholar 

  19. N.C.P. Edirisinghe. New second-order bounds on the expectation of saddle functions with applications to stochastic linear programming. Operations Research, 44:909–922, 1996.

    Article  MATH  Google Scholar 

  20. N.C.P. Edirisinghe and W.T. Ziemba. Bounds for two-stage stochastic programs with fixed recourse. Mathematics of Operations Research, 19:292–313, 1994.

    Article  MathSciNet  MATH  Google Scholar 

  21. H.P. Edmundson. Bounds on the expectation of a convex function of a random variable. Technical Report 982, RAND Corporation, 1957.

    Google Scholar 

  22. D. Eichhorn, F. Gupta, and E. Stubbs. Using constraints to improve the robustness of asset allocation. Journal of Portfolio Management, 24:41–48, 1998.

    Article  Google Scholar 

  23. S.-E. Fleten, K. Hoyland, and S.W. Wallace. The performance of stochastic dynamic and fixed mix portfolio models. Working paper, Norwegian University of Science and Technology, Trondheim, 1998.

    Google Scholar 

  24. B. Forrest, K. Frauendorfer, and M. Schürle. A stochastic optimization model for the investment of savings account deposits. In: P. Kischka et al. (eds.), Operations Research Proceedings 1997, pp. 382–387, Springer, 1998.

    Chapter  Google Scholar 

  25. E. Fragnière, J. Gondzio, and J.-P. Vial. A planning model with one million scenarios solved on an affordable parallel machine. Technical Report 1998.11, Logilab, University of Geneva, 1998.

    Google Scholar 

  26. K. Frauendorfer. Solving SLP recourse problems with arbitrary multivariate distributions: The dependent case. Mathematics of Operations Research, 13:377–394, 1988.

    Article  MathSciNet  MATH  Google Scholar 

  27. K. Frauendorfer. Stochastic Two-Stage Programming. Springer, 1992.

    Book  MATH  Google Scholar 

  28. K. Frauendorfer. Multistage stochastic programming: Error analysis for the convex case. ZOR — Mathematical Methods of Operations Research, 39:93–122, 1994.

    Article  MathSciNet  MATH  Google Scholar 

  29. K. Frauendorfer. Barycentric scenario trees in convex multistage stochastic programming. Mathematical Programming, 75:277–293, 1996.

    MathSciNet  MATH  Google Scholar 

  30. K. Frauendorfer and G. Haarbriicker. Test problems in stochastic multistage programming. Optimization, to appear.

    Google Scholar 

  31. K. Frauendorfer and F. Härtel. On the goodness of discretizing diffusion processes for stochastic programming. Working paper, Institute of Operations Research, University of St. Gallen, 1995.

    Google Scholar 

  32. K. Frauendorfer and P. Kail. A solution method for SLP recourse problems with arbitrary multivariate distributions: The independent case. Problems of Control and Information Theory, 17:177–205, 1988.

    MATH  Google Scholar 

  33. K. Frauendorfer and C. Marohn. Refinement issues in stochastic multistage linear programming. In: K. Marti and P. Kail (eds.), Stochastic Programming Methods and Technical Applications (Proceedings of the 3rd GAMM/IFIP Workshop 1996), pp. 305–328, Springer, 1998.

    Chapter  Google Scholar 

  34. K. Frauendorfer, C. Marohn, and M. Schürle. SG-portfolio test problems for stochastic multistage linear programming (II). Working paper, Institute of Operations Research, University of St. Gallen, 1997.

    Google Scholar 

  35. K. Frauendorfer and M. Schürle. Barycentric approximation of stochastic interest rate processes. In: W.T. Ziemba and J.M. Mulvey (eds.), Worldwide Asset and Liability Modeling, pp. 231–262. Cambridge University Press, Cambridge, 1998.

    Google Scholar 

  36. B. Golub, M. Holmer, R. McKendall, L. Pohlman, and S.A. Zenios. A stochastic programming model for money management. European Journal of Operational Research, 85:282–296, 1995.

    Article  MATH  Google Scholar 

  37. T. Hakala. A Stochastic Optimization Model for Multi-Currency Bond Portfolio ManagementPhd thesis, Helsinki School of Economics and Business Administration, 1996.

    Google Scholar 

  38. J.L. Higle and S. Sen. Stochastic Decomposition — A Statistical Method for Large Scale Stochastic Linear Programming. Kluwer, 1996.

    MATH  Google Scholar 

  39. T. Ho. Key rate durations: Measures of interest rate risks. Journal of Fixed Income, 2:29–44, 1992.

    Article  Google Scholar 

  40. M.R. Holmer. The asset-liability management strategy system at Fannie Mae. Interfaces, 24:3–21, 1994.

    Article  Google Scholar 

  41. R.A. Jarrow and D.R. van Deventer. The arbitrage-free valuation and hedging of demand deposits and credit card loans. Journal of Banking and Finance, 22:249–272, 1998.

    Article  Google Scholar 

  42. J.L. Jensen. Sur les fonctions convexes et les inégalités entre les valeurs moyennes. Acta Mathematica, 30:175–193, 1906.

    Article  MathSciNet  MATH  Google Scholar 

  43. P. Kall, A. Ruszczynski, and K. Frauendorfer. Approximation techniques in stochastic programming. In: Y. Ermoliev and R.J.-B. Wets (eds.), Numerical Techniques for Stochastic Optimization, pp. 33–64. Springer, 1988.

    Chapter  Google Scholar 

  44. J.G. Kallberg, R.W. White, and W.T. Ziemba. Short term financial planning under uncertainty. Management Science, 28:670–682, 1982.

    Article  MATH  Google Scholar 

  45. M.I. Kusy and W.T. Ziemba. A bank asset and liability management model. Operations Research, 34:356–376, 1986.

    Article  Google Scholar 

  46. R. Litterman and J. Scheinkman. Common factors affecting bond returns. Journal of Fixed Income, 1:54–61, 1991.

    Article  Google Scholar 

  47. A. Madansky. Bounds on the expectation of a convex function of a multivariate random variable. Annals of Mathematical Statistics, 30:743–746, 1959.

    Article  MathSciNet  MATH  Google Scholar 

  48. H.M. Markowitz. Portfolio Selection: Efficient Diversification of Investment. Wiley, 1959.

    Google Scholar 

  49. J.M. Mulvey. Financial planning via multi-stage stochastic programs. In: J.R. Birge and K.G. Murty (eds.), Mathematical Programming: State of the Art 1994, pp. 151–171. University of Michigan, Ann Arbor, 1994.

    Google Scholar 

  50. J.M. Mulvey. Multi-stage financial planning systems. In: R.L. D’Ecclesia and S.A. Zenios (eds.), Operations Research Models in Quantitative Finance, pp. 18–35. Physica, 1994.

    Chapter  Google Scholar 

  51. J.M. Mulvey and A. Ruszczynski. A new scenario decomposition method for large-scale stochastic optimization. Operations Research, 43:477–490, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  52. J.M. Mulvey and A.E. Thorlacius. The Towers Perrin global capital market scenario generation system. In: W.T. Ziemba and J.M. Mulvey (eds.), Worldwide Asset and Liability Modeling, pp. 286–312. Cambridge University Press, 1998.

    Google Scholar 

  53. J.M. Mulvey and S.A. Zenios. Capturing the correlations of fixed-income instruments. Management Science, 40:1329–1342, 1994.

    Article  MATH  Google Scholar 

  54. R. T. Rockafellar and R.J.-B. Wets. Nonanticipativity and L 1-martingales in stochastic optimization problems. Mathematical Programming Study, 6:170–187, 1976.

    Article  MathSciNet  Google Scholar 

  55. C.H. Rosa and A. Ruszczynski. On augmented Lagrangian decomposition methods for multistage stochastic programs. Annals of Operations Research, 64:289–309, 1996.

    Article  MathSciNet  MATH  Google Scholar 

  56. A. Ruszczynski. On the regularized decomposition method for stochastic programming problems. In: K. Marti and P. Kail (eds.), Stochastic Programming: Numerical Techniques and Engineering Applications, pp. 93–108, Springer, 1993.

    Google Scholar 

  57. A. Ruszczynski. Parallel decomposition of multistage stochastic programming problems. Mathematical Programming, 58:201–228, 1993.

    Article  MathSciNet  MATH  Google Scholar 

  58. A. Ruszczynski. Decomposition methods in stochastic programming. Mathematical Programming, 79:333–353, 1997.

    MathSciNet  MATH  Google Scholar 

  59. A. Ruszczynski and A. Swiçtanowski. On the regularized decomposition method for two-stage stochastic linear problems. Working Paper WP-96–014, IIASA, Laxenburg, 1996.

    Google Scholar 

  60. M. Schürle. Zinsmodelle in der stochastischen Optimierung. Haupt, 1998.

    Google Scholar 

  61. M. Steinbach. Recursive direct algorithms for multistage stochastic programs in financial engineering. In: P. Kail and H.-J. Lüthi (eds.), Operations Research Proceedings 1998, pp. 241–250, Springer, 1999.

    Chapter  Google Scholar 

  62. P. Varaiya and R.J.-B. Wets. Stochastic dynamic optimization — approaches and computation. Working Paper WP-88–87, IIASA, Laxenburg, 1988.

    Google Scholar 

  63. O. Vasicek. An equilibrium characterization of the term structure. Journal of Financial Economics, 5:177–188, 1977.

    Article  Google Scholar 

  64. C. Vassiadou-Zeniou and S.A. Zenios. Robust optimization models for managing callable bond portfolios. European Journal of Operational Research, 91:264–273, 1996.

    Article  MATH  Google Scholar 

  65. K.J. Worzel, C. Vassiadou-Zeniou, and S.A. Zenios. Integrated simulation and optimization models for tracking indices of fixed-income securities. Operations Research, 42:223–233, 1994.

    Article  MATH  Google Scholar 

  66. S.A. Zenios. A model for portfolio management with mortgage-backed securities. Annals of Operations Research, 43:337–356, 1993.

    Article  MathSciNet  MATH  Google Scholar 

  67. S.A. Zenios. Asset/liability management under uncertainty for fixed-income securities. Annals of Operations Research, 59:77–97, 1995.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Frauendorfer, K., Schürle, M. (2000). Stochastic Optimization in Asset & Liability Management: A Model for Non-Maturing Accounts. In: Uryasev, S.P. (eds) Probabilistic Constrained Optimization. Nonconvex Optimization and Its Applications, vol 49. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3150-7_4

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-3150-7_4

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-4840-3

  • Online ISBN: 978-1-4757-3150-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics