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On entropy martingale optimal transport theory

Author

Listed:
  • Alessandro Doldi

    (Università degli Studi di Firenze)

  • Marco Frittelli

    (Università degli Studi di Milano)

  • Emanuela Rosazza Gianin

    (Università degli Studi di Milano Bicocca)

Abstract

In this paper, we give an overview of (nonlinear) pricing-hedging duality and of its connection with the theory of entropy martingale optimal transport (EMOT), recently developed, and that of convex risk measures. Similarly to Doldi and Frittelli (Finance Stoch 27(2):255–304, 2023), we here establish a duality result between a convex optimal transport and a utility maximization problem. Differently from Doldi and Frittelli (Finance Stoch 27(2):255–304, 2023), we provide here an alternative proof that is based on a compactness assumption. Subhedging and superhedging can be obtained as applications of the duality discussed above. Furthermore, we provide a dual representation of the generalized optimized certainty equivalent associated with indirect utility.

Suggested Citation

  • Alessandro Doldi & Marco Frittelli & Emanuela Rosazza Gianin, 2024. "On entropy martingale optimal transport theory," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 47(1), pages 1-42, June.
    • Handle: RePEc:spr:decfin:v:47:y:2024:i:1:d:10.1007_s10203-023-00432-y
    DOI: 10.1007/s10203-023-00432-y
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    References listed on IDEAS

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    More about this item

    Keywords

    Martingale optimal transport; Entropy optimal transport; Pricing-hedging duality; Robust finance; Pathwise finance;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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