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Solving Nonlinear Programming Problems With Stochastic Objective Functions

In: Selected Works of William T Ziemba A Memorial Volume

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  • William T. Ziemba

Abstract

In many nonlinear programming applications the objective function has an inherent uncertainty that depends upon a set of random variables that have a known distribution. If one wishes to optimize the expectation of the objective, as suggested by the expected utility theorem, then as is shown here one can often solve such problems by modifying standard nonlinear programming algorithms. To illustrate what is involved, the details and justification for the application of the interior parametric sequential unconstrained maximization technique and the generalized programming method for the solution of such problems are given. Some related problems with stochastic constraints for which the solution method applies are mentioned and an example of a portfolio selection problem is given.

Suggested Citation

  • William T. Ziemba, 2024. "Solving Nonlinear Programming Problems With Stochastic Objective Functions," World Scientific Book Chapters, in: Leonard MacLean & Sébastien Lleo (ed.), Selected Works of William T Ziemba A Memorial Volume, chapter 2, pages 25-43, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789811285530_0002
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    Keywords

    William Ziemba; Financial Planning Models; Racetrack Betting; Sports Analytics; Market Anomalies; Risk Factors;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

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