On entropy martingale optimal transport theory

Alessandro Doldi (), Marco Frittelli () and Emanuela Rosazza Gianin ()
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Alessandro Doldi: Università degli Studi di Firenze
Marco Frittelli: Università degli Studi di Milano
Emanuela Rosazza Gianin: Università degli Studi di Milano Bicocca

Decisions in Economics and Finance, 2024, vol. 47, issue 1, No 1, 42 pages

Abstract: 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.

Keywords: Martingale optimal transport; Entropy optimal transport; Pricing-hedging duality; Robust finance; Pathwise finance; 49Q25; 49J45; 60G46; 91G80; 90C46 (search for similar items in EconPapers)
JEL-codes: C61 G13 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10203-023-00432-y

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