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Approximation with Independent Variables

In: Peter Carr Gedenkschrift Research Advances in Mathematical Finance

Author

Listed:
  • Freddy Delbaen
  • Chitro Majumdar

Abstract

Given a square integrable m-dimensional random variable X on a probability space (Ξ©, β„±, β„™) and a sub sigma-algebra π’œ, we show that there exists another m-dimensional random variable Y, independent of π’œ and minimizing the L2 distance to X. Such results have an importance to fairness and bias reduction in artificial intelligence, machine learning and network theory.

Suggested Citation

  • Freddy Delbaen & Chitro Majumdar, 2023. "Approximation with Independent Variables," World Scientific Book Chapters, in: Robert A Jarrow & Dilip B Madan (ed.), Peter Carr Gedenkschrift Research Advances in Mathematical Finance, chapter 9, pages 311-327, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789811280306_0009
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    Cited by:

    1. Capaldo, Marco & Di Crescenzo, Antonio & Pellerey, Franco, 2024. "Generalized Gini’s mean difference through distortions and copulas, and related minimizing problems," Statistics & Probability Letters, Elsevier, vol. 206(C).

    More about this item

    Keywords

    Mathematical Finance; Quantitative Finance; Option Pricing; Derivatives; No Arbitrage; Asset Price Bubbles; Asset Pricing; Equilibrium; Volatility; Diffusion Processes; Jump Processes; Stochastic Integration; Trading Strategies; Portfolio Theory; Optimization; Securities; Bonds; Commodities; Futures;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

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