For the sake of completeness, we first present the Sinkhorn’s theorem and explain how it was used to derive the solution of the regularized optimal transport. Theorem ((Sinkhorn & Knopp, 1967)). If A is an n × n matrix with strictly positive elements, then there exist diagonal matrices D1 and D2 with strictly positive diagonal elements such that D1 ∗ A ∗ D2 is doubly stochastic. The matrices D1...

Since Pardoux and Peng firstly studied the following nonlinear backward stochastic differential equations in 1990. The theory of BSDE has been widely studied and applied, especially in the stochastic control, stochastic differential games, financial mathematics and partial differential equations. In 1994, Pardoux and Peng came up with backward doubly stochastic differential equations to give th...

Introduction. A classical result in the theory of convex polyhedra is that every bounded polyhedral convex set can be expressed either as the intersection of half-spaces or as a convex combination of extreme points. It is becoming increasingly apparent that a full understanding of a class of convex polyhedra requires the knowledge of both of these characterizations. Perhaps the earliest and nea...

We study a hedging and pricing problem of a model where the price process of a risky asset has jumps with instantaneous feedback from the most recent asset price. We model these jumps with a doubly stochastic Poisson process with an intensity function depending on the current price. We find a closed form expression of the local risk minimization strategy using Föllmer and Schweizer decompositio...

In this study, we give a characterization of all torsion units which are in the unit group of ZS3 integral group ring of symmetric group S3, and classify conjugate classes of these units. We used the group of all doubly stochastic matrices in GL(3,Z) in this classification. The investigation of torsion units is not restricted with this study, and the classification of torsion units of bigger or...

A determinantal approximation is obtained for the permanent of a doubly stochastic matrix. For moderate-deviation matrix sequences, the asymptotic relative error is of order O(n−1). keywords: Doubly stochastic Dirichlet distribution; Maximum-likelihood projection; Sinkhorn projection