Epi-convergent discretizations of multistage stochastic programs via integration quadratures

Mathematical Programming

Volumn 116, Issue 1-2, 2009, Pages 461-479

  Pennanen, Teemu ^a  

^a HELSINKI SCHOOL OF ECONOMICS   (Finland)

Author keywords

Discretization; Epi convergence; Quadrature; Stochastic programming

Indexed keywords

AEROSPACE APPLICATIONS; INTEGRATION; NONLINEAR PROGRAMMING; NUMERICAL ANALYSIS; NUMERICAL METHODS; STOCHASTIC MODELS; TIME SERIES ANALYSIS; VARIATIONAL TECHNIQUES;

CLUSTER POINTS; CONVEX OPTIMIZATION; DISCRETIZATION; DISCRETIZATIONS; DISCRETIZED PROBLEMS; EFFICIENT IMPLEMENTATION; EPI-CONVERGENCE; GENERAL CLASS; NUMERICAL INTEGRATIONS; ORIGINAL PROBLEM; SPRINGER (CO); TIME SERIES MODELING; UNCERTAIN FACTORS; VARIATIONAL INEQUALITIES;

STOCHASTIC PROGRAMMING;

EID: 45749127048     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-007-0113-9     Document Type: Article

References (53)

1. Attouch H. (1984). Variational Convergence for Functions and Operators. Pitman (Advanced Publishing Program), Boston
2. Back K., Pliska S.R. (1987). The shadow price of information in continuous time decision problems. Stochastics 22(2): 151-186
3. Billingsley P. (1995). Probability and measure. 3rd edn. Wiley Series in Probability and Mathematical Statistics. Wiley, New York
4. Billingsley P. (1999). Convergence of probability measures, 2nd edn. Wiley, New York
5. Black F., Karasinski P. (1991). Bond and option pricing when short rates are lognormal. Finan. Anal. J. July-August: 52-59
6. Boender, C.G.E., van Aalst, P., Heemskerk, F.: Modelling and management of assets and liabilities of pension plans in The Netherlands. In: Ziemba W.T., Mulvey J.M. (eds.) Worldwide asset and liability modeling, pp. Cambridge University Press 561-580 (1998)
7. Braides, A.: Γ for beginners. Oxford Lecture Series in Mathematics and its Applications, vol. 22. Oxford University Press, Oxford
8. Casey M., Sen S. (2005). The scenario generation algorithm for multistage stochastic linear programs. Math. Oper. Res. 30(3): 615-631
9. Chen X., Womersley R.S. (1996). A parallel inexact Newton method for stochastic programs with recourse. Ann. Oper. Res. 64: 113-141
10. Chiralaksanakul, A.: Monte carlo methods for multi-stage stochastic programs. PhD thesis, University of Texas at Austin, Texas (2003)
11. Clements M.P., Hendry D.F. (1999). Forecasting Non-Stationary Economic Time Series. MIT Press, Cambridge
12. Dal Maso, G.: An introduction to Γ-convergence, Progress in Nonlinear Differential Equations and their Applications, vol. 8. Birkhäuser Boston Inc., Boston (1993)
13. Dempster M.A.H., Germano M., Medova E., Villaverde M. (2003). Global asset liability management. Br. Actuar. J. 9(1): 137-195
14. Dupačová J., Consigli G., Wallace S.W. (2001). Scenarios for multistage stochastic programs. Ann. Oper. Res. 100: 25-53
15. Dupačová J., Gröwe-Kuska N., Römisch W. (2003). Scenario reduction in stochastic programming. An approach using probability metrics. Math. Program. 95(3, Ser. A): 493-511
16. Engle R.F., Granger C.W.J. (1987). Co-integration and error correction: representation, estimation and testing. Econometrica 55(2): 251-276
17. Folland G.B. (1999). Real analysis, 2nd edn Pure and Applied Mathematics. Wiley, New York
18. Frauendorfer K. (1996). Barycentric scenario trees in convex multistage stochastic programming. Math. Programm. Approximation comput. stoc. Programm. 75(2, Ser. B): 277-293
19. Gondzio J., Kouwenberg R., Vorst T. (2003). Hedging options under transaction costs and stochastic volatility. J. Econ. Dyn. Control 27(6): 1045-1068
20. Heitsch H., Römisch W. (2003). Scenario reduction algorithms in stochastic programming. Comput. Optim. Appl. Stochastic programming 24(2-3): 187-206
21. Heitsch, H., Römisch, W., Strugarek, C.: Stability of multistage stochastic programs. Preprint 255, DFG Research Center Matheon Mathematics for key technologies (2005)
22. Hilli, P., Koivu, M., Pennanen, T., Ranne, A.: A stochastic programming model for asset liability management of a finnish pension company. Ann. Oper. Res. (in press)
23. Hlawka E., Mück R. (1972). Über eine Transformation von gleichverteilten Folgen. II. Computing (Arch. Elektron. Rechnen) 9: 127-138
24. Ioffe A.D. (1977). On lower semicontinuity of integral functionals. I. SIAM J. Control Optimization 15(4): 521-538
25. Kouwenberg R. (2001). Scenario generation and stochastic programming models for asset liability management. Eur. J. Oper. Res. Financ. Model. 134(2): 279-292
26. L'Ecuyer P., Lemieux C. (2000). Variance reduction via lattice rules. Manage. Sci. 46(2): 1214-1235
27. Lepp R. (1990). Approximations to stochastic programs with complete recourse. SIAM J. Control Optim. 28(2): 382-394
28. Lucchetti R., Salinetti G., Wets R.J.B. (1994). Uniform convergence of probability measures: topological criteria. J. Multivariate Anal. 51(2): 252-264
29. Marti, K., Ermoliev, Y., Pflug, G. (eds.): Dynamic stochastic optimization, Lecture Notes in Economics and Mathematical Systems. vol. 532. Papers from the IFIP/IIASA/GAMM Workshop held in Laxenburg, March 11-14, 2002. Springer, Berlin (2004)
30. Marti, K., Kall, P. (eds.): Stochastic programming. Lecture Notes in Economics and Mathematical Systems. vol. 423. Numerical techniques and engineering applications. Springer, Berlin (1995)
31. Marti, K., Kall, P. (eds.): Stochastic programming methods and technical applications. Lecture Notes in Economics and Mathematical Systems. vol. 458. Springer-Verlag, Berlin (1998)
32. Mordukhovich B. (1978). On difference approximations of optimal control systems. J. Appl. Math. Mech 42(3): 431-440
33. Niederreiter, H.: Random number generation and quasi-Monte Carlo methods, CBMS-NSF Regional Conference Series in Applied Mathematics. vol. 63. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (1992)
34. Niederreiter, H. (ed.): Monte Carlo and quasi-Monte Carlo methods 2002. In: Proceedings of a conference held at the National Univeristy of Singapore, Republic of Singapore, November 25-28, 2002. Springer-Verlag, Berlin (2004)
35. Olsen P. (1976). Discretizations of multistage stochastic programming problems. Math. Programm. Stud. 6: 111-124
36. Pennanen T. (2005). Epi-convergent discretizations of multistage stochastic programs. Math. Oper. Res. 30(1): 245-256
37. Pennanen, T., Koivu, M.: Integration quadratures in discretization of stochastic programs. Stochastic Programming E-Print Series (2002)
38. Pennanen T., Koivu M. (2005). Epi-convergent discretizations of stochastic programs via integration quadratures. Numer. Math. 100(1): 141-163
39. Pflug G. (2001). Scenario tree generation for multiperiod financial optimization by optimal discretization. Math. Program. Math. Programm. Finance 89(2, Ser. B): 251-271
40. Pflug, G., Hochreiter, R.: Scenario generation for stochastic multi-stage decision processes as facility location problems. Technical report, Department of Statistics and Decision Support Systems, University of Vienna (2003)
41. Polak, E.: Optimization. Applied Mathematical Sciences. vol. 124. Algorithms and consistent approximations. Springer, New York (1997)
42. Rockafellar R.T., Wets R.J.B. (1974). Continuous versus measurable recourse in N-stage stochastic programming. J. Math. Anal. Appl. 48: 836-859
43. 1-martingales in stochastic optimization problems. Math. Programm. Stud. 6: 170-187
44. Rockafellar R.T., Wets R.J.B. (1977). Measures as Lagrange multipliers in multistage stochastic programming. J. Math. Anal. Appl. 60(2): 301-313
45. Rockafellar, R.T., Wets, R.J.B.: Variational analysis. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] vol. 317. Springer, Berlin (1998)
46. Römisch, W.: Stability of stochastic programming problems. In: Stochastic Programming, Handbooks in Operations Research and Management Science. vol. 10, pp. 483-554. Elsevier, Amsterdam (2003)
47. Ruszczynski, A., Shapiro, A. (eds.): Stochastic Programming, Handbooks in Operations Research and Management Science. vol. 10. Elsevier, Amsterdam (2003)
48. Shapiro A. (2003). Inference of statistical bounds for multistage stochastic programming problems. Math. Methods Oper. Res. 58(1): 57-68
49. Shapiro, A.: On complexity of multistage stochastic programs. Optimization Online (2005)
50. Shiryaev, A.N.: Essentials of stochastic finance, Advanced Series on Statistical Science & Applied Probability. vol. 3. World Scientific Publishing Co. Inc., River Edge(1999)
51. Sloan I.H., Joe S. (1994). Lattice methods for multiple integration. The Clarendon Press/Oxford University Press, New York
52. Vainikko G.M. (1971). The convergence of the method of mechanical quadratures for integral equations with discontinuous kernels. Siberian Math. J. 12: 29-38
53. Ziemba, W.T., Mulvey, J.M. (eds.): Worldwide Asset and Liability Modeling, Publications of the Newton Institute, vol. 10. Cambridge University Press, Cambridge (1998)