Category Rapports

Fév
2017

The financialization of the term structure of risk premia in commodity markets

Edouard Jaeck In this paper, I examine how financialization affects the term structure of risk premia by using an equilibrium model for commodity futures markets. I define financialization as the entry of cross-asset investors, who are exposed to a commodity risk, into a commodity market. Qualitatively, the model shows that the financialization decreases the segmentation …

Jan
2017

Unbiased Monte Carlo estimate of stochastic differential equations expectations

Mahamadou Doumbia, Nadia Oudjane,  Xavier Warin  We propose an unbiased Monte Carlo method to compute E(g(XT ))  where g is a Lipschitz function and X an Ito process. This approach extends the method proposed in [16] to the case where X is solution of a multidimensional stochastic differential equation with varying drift and diffusion …

Oct
2016

Contracting Theory with Competitive Interacting Agents

Romuald Elie, Dylan Possamaï In a framework close to the one developed by Holmstrom and Milgrom [44], we study the optimal contracting scheme between a Principal and several Agents. Each hired Agent is in charge of one project, and can make efforts towards managing his own project, as well as impact (positively or negatively) the …

Sep
2016

A Non-Intrusive Stratified Resampler for Regression Monte Carlo: Application to Solving Non-Linear Equations

EMMANUEL GOBET, GANG LIU, AND JORGE P. ZUBELLI Abstract. Our goal is to solve certain dynamic programming equations associated to a given Markov chain X, using a regression-based Monte Carlo algorithm. More speci cally, we assume that the model for X is not known in full detail and only a root sample X1; : : : ;XM of …

Sep
2016

Pricing American options using martingale bases

J. Lelong In this work, we propose an algorithm to price American options by directly solving the dual minimization problem introduced by Rogers [2002]. Our approach relies on approximating the set of uniformly square integrable martingales by a finite dimensional Wiener chaos expansion. Then, we use a sample average approximation technique to efficiently solve the …

Sep
2016

Volatility in electricity derivative markets: the Samuelson effect revisited

Edouard Jaeck, Delphine Lautier This article proposes an empirical study of the Samuelson effect in electricity markets. Our motivations are twofold. First, although the literature largely assesses the decreasing pattern in the volatilities along the price curve in commodity markets, it has not extensively tested the presence of such a dynamic feature in electricity prices. …

Sep
2016

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 …

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 …

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