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...

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...

We consider the Hamiltonian cycle problem (HCP) embedded in a controlled Markov decision process. In this setting, HCP reduces to an optimization problem on a set of Markov chains corresponding to a given graph. We prove that Hamiltonian cycles are minimizers for the trace of the fundamental matrix on a set of all stochastic transition matrices. In case of doubly stochastic matrices with symmet...

We prove strong uniqueness for a parabolic SPDE involving both the solution v(t, x) and its derivative ∂xv(t, x). The familiar YamadaWatanabe method for proving strong uniqueness might encounter some difficulties here. In fact, the Yamada-Watanabe method is essentially one dimensional, and in our case there are two unknown functions, v and ∂xv. However, Pardoux and Peng’s method of backward dou...

In this paper, for each graphG, we define a chain complex of graded modules over the ring of polynomials, whose graded Euler characteristic is equal to the chromatic polynomial of G. We also define a chain complex of doubly graded modules, whose (doubly) graded Euler characteristic is equal to the dichromatic polynomial of G. Both constructions use Koszul complexes, and are similar to the new K...

ABSTRACT. A bivariate distribution with continuous margins can be uniquely decomposed via a copula and its marginal distributions. We consider the problem of estimating the copula function and adopt a nonparametric Bayesian approach. On the space of copula functions, we construct a finite dimensional approximation subspace which is parameterized by a doubly stochastic matrix. A major problem he...

We are interested in the following work in the doubly stochastic matrix nearness problem. Instances of this problems occurs in differents fields: aggregation of preferences in operational research, calculus of variations and shape optimisation, etc. We propose here a direct study via the projection theorem and a numerical resolution inspired by the alternating projections algorithm of Boyle-Dyk...