Category Rapports

Juil
2016

On the Robustness of the Snell envelope

Pierre Del Moral, Peng Hu, Nadia Oudjane, Bruno Remillard We analyze the robustness properties of the Snell envelope backward evolution equation for the discrete time optimal stopping problem. We consider a series of approximation schemes, including cut-off type approximations, Euler discretization schemes, interpolation models, quantization tree models, and the Stochastic Mesh method of Broadie-Glasserman. In …

Mai
2016

Nonzero-sum Stochastic Differential Games with Impulse Controls and Applications to Retail Energy Markets

RR-Fime-16-05 Rene Aïd, Matteo Basei, Giorgia Callegaro, Luciano Campi, Tiziano Vargiolu We consider a singular control problem with regime switching that arises in problems of optimal investment decisions of cash-constrained firms. The value function is proved to be the unique viscosity solution of the associated Hamilton-Jacobi-Bellman equation. Moreover, we give regularity properties of the value …

Avr
2016

Numerical Approximation of a Cash-Constrained Firm Value with Investment Opportunities

RR-Fime-16-04 Erwan Pierre, Stéphane Villeneuve, Xavier Warin We consider a singular control problem with regime switching that arises in problems of optimal investment decisions of cash-constrained firms. The value function is proved to be the unique viscosity solution of the associated Hamilton-Jacobi-Bellman equation. Moreover, we give regularity properties of the value function as well as …

Mar
2016

Branching Diffusion Representation of Semilinear PDEs and Monte Carlo Approximation

RR-FiME-16-03 Pierre Henry-Labordère, Nadia Oudjane, Xiaolu Tan, Nizar Touzi, Xavier Warin We provide a representation result of parabolic semi-linear PD-Es, with polynomial nonlinearity, by branching diffusion processes. We extend the classical representation for KPP equations, introduced by Skorokhod [23], Watanabe [27] and McKean [18], by allowing for polynomial nonlinearity in the pair (u;Du), where u …

Jan
2016

On the Control of the Difference between two Brownian Motions: A Dynamic Copula Approach

RR-FiME-16-02 Thomas DESCHATRE We propose new copulae to model the dependence between two Brownian motions and to control the distribution of their difference. Our approach is based on the copula between the Brownian motion and its reflection. We show that the class of admissible copulae for the Brownian motions are not limited to the class …

Jan
2016

Computing Expectations for General SDE with Pure Monte Carlo Methods

RR-FIME-16-01 Mahamadou Doumbia, Nadia Oudjane, Xavier Warin We develop a pure Monte Carlo method to compute E(g(XT )) where g is a bounded and Lipschitz function and Xt an Ito process. This approach extends the method proposed in [7] to the general multidimensional case with a SDE with varying coefficients. A variance reduction method relying …

Sep
2015

Stratified Regression Monte-Carlo Scheme For Semilinear PDES and BSDES with Large Scale Parallelization on GPUS

RR-FiME-15-04 E. GOBET, J. G. LOPEZ-SALAS, P. TURKEDJIEV, AND C. VAZQUEZ In this paper, we design a novel algorithm based on Least-Squares Monte Carlo (LSMC) in order to approximate the solution of discrete time Backward Stochastic Differential Equations (BSDEs). Our algorithm allows massive parallelization of the computations on multicore devices such as graphics processing units …

Avr
2015

Probabilistic Representation of a Class of Non Conservative Nonlinear Partial Differential Equations

RR-FiME-15-02 Anthony LECAVIL, Nadia OUDJANE and Francesco RUSSO We introduce a new class of nonlinear Stochastic Differential Equations in the sense ofMcKean, related to non conservative nonlinear Partial Differential equations (PDEs). We discuss existence and uniqueness pathwise and in law under various assumptions. We propose an original interacting particle system for which we discuss the …

Fév
2015

Strategic Capacity Investment under Hold-up Threats: The Role of Contract Length and Width

RR-FiME-15-05 Laure Durand-Viel and Bertrand Villeneuve We analyze the impact of the length of incomplete contracts on investment and surplus sharing. In the bilateral relationship explored, the seller controls the input and the buyer invests. With two-part tariffs, the length of the contract is irrelevant: the surplus is maximal and goes to the seller. In …

Jan
2015

Does France Have a Fuel Poverty Trap?

RR-FiME-15-01 Corinne CHATON In this article, we focus on fuel poverty. More specifically, we analyse this phenomenon‟s dynamic by answering the following question: does France have a fuel poverty trap? First, we define three states/situations into which individuals may be placed: the non-fuel poverty state, the fuel poverty state and the severe fuel poverty state. …

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