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A Result on Integral Functionals with Infinitely Many Constraints

Author

Listed:
  • Tahir CHOULLI

    (University of Alberta)

  • Martin SCHWEIZER

    (ETH Zurich and Swiss Finance Institute)

Abstract

A classic paper of Borwein/Lewis (1991) studies optimisation problems over L^p_+ with finitely many linear equality constraints, given by scalar products with functions from L^q. One key result shows that if some x in L^p_+ satisfies the constraints and if the constraint functions are pseudo-Haar, the constraints can also be realised by another function y in the interior of L^\infty_+ . We establish an analogue of this result in a setting with infinitely many, measurably parametrised constraints, and we briefly sketch an application in arbitrage theory.

Suggested Citation

  • Tahir CHOULLI & Martin SCHWEIZER, 2015. "A Result on Integral Functionals with Infinitely Many Constraints," Swiss Finance Institute Research Paper Series 15-38, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp1538
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    File URL: http://ssrn.com/abstract=2662476
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    Cited by:

    1. Tahir CHOULLI & Martin SCHWEIZER, 2015. "Locally Phi-Integrable Sigma-Martingale Densities for General Semimartingales," Swiss Finance Institute Research Paper Series 15-15, Swiss Finance Institute.

    More about this item

    Keywords

    linear equality constraints; feasible solution; infinitely many constraints; random measure; arbitrage theory; equivalent martingale measures;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • Z00 - Other Special Topics - - General - - - General

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