Archives

8
Sep

Forward Feynman-Kac Type Representation for Semilinear Nonconservative Partial Differential Equations

Anthony LE CAVIL, Nadia OUDJANE and Francesco RUSSO We propose a nonlinear forward Feynman-Kac type equation, which represents the solution of a nonconservative semilinear parabolic Partial Differential Equations (PDE). We show in particular existence and uniqueness in the first part of the article. The second part is devoted to the construction of a probabilistic particle algorithm and the …

26
Juil

Technology transition to electric mobility

R. Aïd, I. Ben Tahar In Commodities, Energy and Environmental Finance, ed. M. Ludkovki, R. Sircar & R. Aïd, Fields Institute Communication Series, Springer, 2015.  

6
Juil

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 …

1
Juil

Clémence Alasseur

Work in progress [1] Selection adverse and application to electricity tarification with I. Ekeland, R. Elie, Nicolás Hernández Santibáñez and D. Possomai [2] Structural price model for electricity coupled markets with O. Féron [3] An extended Mean Field Game for Storages in Smart Grid with I. Ben Tahar and A. Matoussi [4] Output Hedging of ...
1
Mai

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 …

1
Avr

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 …

1
Mar

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 …

1
Jan

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 …

1
Jan

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 …

1
Sep

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 …

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