The dual representation of the martingale optimal transport problem in the Skorokhod space of multi dimensional càdlàg processes is proved. The dual is a minimization problem with constraints involving stochastic integrals and is similar to the Kantorovich dual of the standard optimal transport problem. The constraints are required to hold for very path in the Skorokhod space. This problem has ...

The current paper explores the potential of areas between mathematics and poetry. We will first recall some definitions results that are needed to construct solutions Yang–Baxter equation. A new duality principle is presented Boolean coalgebras introduced. section on poetry dedicated equation presented, a discussion poem related mathematical formula follows. final presents our conclusions furth...

We discuss two approaches to duality for multiple objective linear problems. The first approach is based on a duality relation between a set and its complement in the outcome space. It allows us to obtain a number of known duality constructions. The second approach utilizes polarity between a polyhedral set and the epigraph of its support function. It leads to a parametric dual problem which is...

In this paper, we study a pair of fuzzy primal–dual linear programming problems and calculate duality results using an aspiration level approach. We use an exponential membership function, which is in contrast to the earlier works that relied on a linear membership function. As the fuzzy environment causes a duality gap, we investigate how choosing the exponential membership function impacts th...

This online supplement provides additional material to accompany the printed paper, henceforth denoted ES. In Section S.1, we review some mathematical background on Fenchel duality used in the proof of the representation and uniqueness results in ES. In Section S.2, we establish the necessity of the L-continuity axiom for the signed RFCC representation defined in Appendix C. Section S.3 include...

Let G be a locally compact group. We show that the category A(G) of actions of G on C∗-algebras (with equivariant nondegenerate ∗-homomorphisms into multiplier algebras) is equivalent, via a full-crossed-product functor, to a comma category of maximal coactions of G under the comultiplication (C∗(G), δG); and also that A(G) is equivalent, via a reduced-crossed-product functor, to a comma catego...

We study utility maximization problem for general utility functions using dynamic programming approach. We consider an incomplete financial market model, where the dynamics of asset prices are described by an R-valued continuous semimartingale. Under some regularity assumptions we derive backward stochastic partial differential equation (BSPDE) related directly to the primal problem and show th...

Very recently, Gudder has given the mathematical theory for the duality computer [1]. In his timely work, he has provided two descriptions, one is in the pure state formalism and the other is in the mixed state formalism for the mathematics of duality computer. The duality computer is a new type of computing machine based on the general principle of quantum interference proposed in Ref.[2]. Not...

Optimal transportation with capacity constraints, a variant of the well-known optimal transportation problem, is concerned with transporting one probability density f ∈ L1(Rm) onto another one g ∈ L1(Rn) so as to optimize a cost function c ∈ L1(Rm+n) while respecting the capacity constraints 0 ≤ h ≤ h̄ ∈ L∞(Rm+n). A linear programming duality theorem for this problem was first established by Lev...

Very recently, Gudder has given the mathematical theory for the duality computer [1]. In his timely work, he has provided two descriptions, one is in the pure state formalism and the other is in the mixed state formalism for the mathematics of duality computer. The duality computer is a new type of computing machine based on the general principle of quantum interference proposed in Ref.[2]. Not...