From entropic transport to martingale transport, and applications to model calibration

TL;DR

This paper introduces a discrete-time semi-martingale optimal transport framework using multi-marginal entropic transport, enabling efficient numerical calibration and connecting to continuous processes as the time step diminishes.

Contribution

It develops a novel discrete-time formulation of semi-martingale optimal transport based on multi-marginal entropic transport and extends Sinkhorn algorithms for calibration tasks.

Findings

Provides a new numerical approach for model calibration

Recovers continuous semi-martingale processes in the limit

Connects entropic transport with semi-martingale optimal transport

Abstract

We propose a discrete time formulation of the semi-martingale optimal transport problem based on multi-marginal entropic transport. This approach offers a new way to formulate and solve numerically the calibration problem proposed by [17], using a multi-marginal extension of Sinkhorn algorithm as in [6, 10, 7]. When the time step goes to zero we recover, as detailed in the companion paper [8], a continuous semi-martingale process, solution to a semi-martingale optimal transport problem, with a cost function involving the so-called 'specific entropy' , introduced in [13], see also [12] and [2].