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Recursive Direct Algorithms for Multistage Stochastic Programs in Financial Engineering

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Operations Research Proceedings 1998

Part of the book series: Operations Research Proceedings 1998 ((ORP,volume 1998))

Summary

Multistage stochastic programs can be seen as discrete optimal control problems with a characteristic dynamic structure induced by the scenario tree. To exploit that structure, we propose a highly efficient dynamic programming recursion for the computationally intensive task of KKT systems solution within an interior point method. Test runs on a multistage portfolio selection problem demonstrate the performance of the algorithm.

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References

  1. A. J. Berger, J. M. Mulvey, E. Rothberg, and R. J. Vanderbei, Solving multistage stochastic programs using tree dissection, Technical Report SOR-95-07, Princeton University, June 1995.

    Google Scholar 

  2. A. J. Berger, J. M. Mulvey, and A. Ruszczynński, An extension of the DQA algorithm to convex stochastic programs, SIAM J. Optimization, 4 (1994), pp. 735–753.

    Article  Google Scholar 

  3. J. R. BlRGE, Decomposition and partitioning methods for multistage stochastic linear programs, Oper. Res., 33 (1985), pp. 989–1007.

    Article  Google Scholar 

  4. J. R. Birge, C. J. Donohue, D. F. Holmes, and O. G. Svintsitski, A parallel im plementation of the nested decomposition algorithm for multistage stochastic linear programs, Math. Programming, 75 (1996), pp. 327–352.

    Google Scholar 

  5. J. Czyzyk, R. FOURER, and S. Mehrotra, A study of the augmented system and columnsplitting approaches for solving two-stage stochastic linear programs by interior-point methods, ORSA J. Computing, 7 (1995), pp. 474–490.

    Article  Google Scholar 

  6. G. B. Dantzig and G. Infanger, Multi-stage stochastic linear programs for portfolio optimization, Annals Oper. Res., 45 (1993), pp. 59–76.

    Article  Google Scholar 

  7. E. A. Eschenbach, C. A. Shoemaker, and H. M. Caffey, Parallel algorithms for stochastic dynamic programming with continuous state and control variables, ORSA J. Computing, 7 (1995), pp. 386–401.

    Article  Google Scholar 

  8. K. Frauendorfer, The stochastic programming extension of the Markowitz approach, Int. J. Mass-Parallel Comput. Inform. Syst., 5 (1995), pp. 449–460.

    Google Scholar 

  9. H. I. Gassmann, MSLiP: A computer code for the multistage stochastic linear programming problem, Math. Programming, 47 (1990), pp. 407–423.

    Article  Google Scholar 

  10. E. R. Jessup, D. Yang, and S. A. Zenios, Parallel factorization of structured matrices arising in stochastic programming, SIAM J. Optimization, 4 (1994), pp. 833–846.

    Article  Google Scholar 

  11. H. M. Markowitz, Portfolio Selection: Efficient Diversification of Investments, John Wiley, New York, 1959.

    Google Scholar 

  12. J. M. Mulvey, Nonlinear network models in finance, Adv. Math. Progr. Fin. Planning, 1(1987), p. 253.

    Google Scholar 

  13. J. M. Mulvey and A. Ruszczyński, A new scenario decomposition method for large-scale stochastic optimization, Oper. Res., 43 (1995), pp. 477–490.

    Article  Google Scholar 

  14. J. M. Mulvey and H. Vladimirou, Stochastic network optimization models for investment planning, Annals Oper. Res., 20 (1989), pp. 187–217.

    Article  Google Scholar 

  15. J. M. Mulvey and H. Vladimirou Applying the progressive hedging algorithm to stochastic generalized networks, Annals Oper. Res., 31 (1991), pp. 399–424.

    Google Scholar 

  16. R. T. Rockafellar and R. J.-B. Wets, Generalized linear-quadratic problems of deterministic and stochastic optimal control in discrete time, SIAM J. Control Optim., 28 (1990), pp. 810–822.

    Article  Google Scholar 

  17. R. T. Rockafellar and R. J.-B. Wets, Scenarios and policy aggregation in optimization under uncertainty, Math. Oper. Res., 16 (1991), pp. 119–147.

    Article  Google Scholar 

  18. A. Ruszczyński, Parallel decomposition of multistage stochastic programming problems, Math. Programming, 58 (1993), pp. 201–228.

    Article  Google Scholar 

  19. A. Ruszczyński, Decomposition methods in stochastic programming, Math. Programming, 79 (1997),pp. 333–353. Invited lectures of the 16th International Symposium on Mathematical Programming, Lausanne EPFL.

    Google Scholar 

  20. M. C. Steinbach, Back to the roots: recursive optimization on dynamic trees. In preparation.

    Google Scholar 

  21. M. C. Steinbach, Recursive direct optimization and successive refinement in multistage stochastic programs.In preparation.

    Google Scholar 

  22. M. C. Steinbach, Fast Recursive SQP Methods for Large-Scale Optimal Control Problems, Ph. D. dissertation, University of Heidelberg, 1995.

    Google Scholar 

  23. M. C. Steinbach, Structured interior point SQP methods in optimal control, Z. Angew. Math. Mech., 76(1996), pp. 59–62.

    Article  Google Scholar 

  24. M. C. Steinbach, H. G. Bock, G. V. Kostin, and R. W. Longman, Mathematical optimization in robotics: Towards automated high speed motion planning, Surv. Math. Ind., 7 (1998), pp. 303–340.

    Google Scholar 

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© 1999 Springer-Verlag Berlin Heidelberg

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Steinbach, M.C. (1999). Recursive Direct Algorithms for Multistage Stochastic Programs in Financial Engineering. In: Kall, P., Lüthi, HJ. (eds) Operations Research Proceedings 1998. Operations Research Proceedings 1998, vol 1998. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58409-1_24

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  • DOI: https://doi.org/10.1007/978-3-642-58409-1_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65381-3

  • Online ISBN: 978-3-642-58409-1

  • eBook Packages: Springer Book Archive

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