Discretizing a backward stochastic differential equation.
Distinguishing and integrating aleatoric and epistemic variation in uncertainty quantification
Much of uncertainty quantification to date has focused on determining the effect of variables modeled probabilistically, and with a known distribution, on some physical or engineering system. We develop methods to obtain information on the system when the distributions of some variables are known exactly, others are known only approximately, and perhaps others are not modeled as random variables at all.The main tool used is the duality between risk-sensitive integrals and relative entropy, and we...
Distributions, noyaux, symboles, d'après Kree
Distributions of functionals of diffusions with jumps.
Distributions sur l'espace de P. Lévy et calcul stochastique
Distribution-valued iterated gradient and chaotic decompositions of Poisson jump times functionals.
We define a class of distributions on Poisson space which allows to iterate a modification of the gradient of [1]. As an application we obtain, with relatively short calculations, a formula for the chaos expansion of functionals of jump times of the Poisson process.
Distribution-Valued Processes Arising from Independent Brownian Motions.
Donsker-type theorem for BSDEs.
Double-barriers-reflected BSDEs with jumps and viscosity solutions of parabolic integrodifferential PDEs.
Doubly reflected BSDEs with call protection and their approximation
We study the numerical approximation of doubly reflected backward stochastic differential equations with intermittent upper barrier (RIBSDEs). These denote reflected BSDEs in which the upper barrier is only active on certain random time intervals. From the point of view of financial interpretation, RIBSDEs arise as pricing equations of game options with constrained callability. In a Markovian set-up we prove a convergence rate for a time-discretization scheme by simulation to an RIBSDE. We also...
Duality of chordal SLE, II
We improve the geometric properties of processes derived in an earlier paper, which are then used to obtain more results about the duality of SLE. We find that for κ∈(4, 8), the boundary of a standard chordal SLE(κ) hull stopped on swallowing a fixed x∈ℝ∖{0} is the image of some trace started from a random point. Using this fact together with a similar proposition in the case that κ≥8, we obtain a description of the boundary of a standard chordal SLE(κ) hull for κ>4, at a finite stopping...
Dynamic analysis of stochastic reaction-diffusion Cohen-Grossberg neural networks with delays.
Dynamic programming and mean-variance hedging in discrete time.
Dynamic Programming for the stochastic Navier-Stokes equations
We solve an optimal cost problem for a stochastic Navier-Stokes equation in space dimension 2 by proving existence and uniqueness of a smooth solution of the corresponding Hamilton-Jacobi-Bellman equation.
Dynamic programming principle for stochastic recursive optimal control problem with delayed systems
In this paper, we study one kind of stochastic recursive optimal control problem for the systems described by stochastic differential equations with delay (SDDE). In our framework, not only the dynamics of the systems but also the recursive utility depend on the past path segment of the state process in a general form. We give the dynamic programming principle for this kind of optimal control problems and show that the value function is the viscosity solution of the corresponding infinite dimensional...
Dynamic term structure modelling with default and mortality risk: new results on existence and monotonicity
This paper considers dynamic term structure models like the ones appearing in portfolio credit risk modelling or life insurance. We study general forward rate curves driven by infinitely many Brownian motions and an integer-valued random measure, generalizing existing approaches in the literature. A precise characterization of absence of arbitrage in such markets is given in terms of a suitable criterion for no asymptotic free lunch (NAFL). From this, we obtain drift conditions which are equivalent...
Dynamical systems with multiplicative perturbations
Editorial - Spring School Mons Random differential equations and gaussian fields
EDPS paraboliques à coefficients non—lipschitziens avec réflexion
EDSR, convergence en loi et homogénéisation d'EDP paraboliques semi-linéaires