t and stable multivariate kernel density estimation by fast sum updating - N . Langrené, X. Warin

Kernel density estimation and kernel regression are powerful but computationally expensive techniques: a direct evaluation of kernel density estimates at M evaluation points given N input sample points requires a quadratic O(MN) operations, which is prohibitive for large scale problems. For this reason, approximate methods such as binning with Fast Fourier Transform or the Fast Gauss Transform have been proposed to speed up kernel density estimation. Among these fast methods, the Fast Sum Updating Read more [...]


Monte Carlo for high-dimensional degenerated Semi Linear and Full Non Linear PDEs - X. Warin

We extend a recently developed method to solve semi-linear PDEs to the case of a degenerated diffusion. Being a pure Monte Carlo method it does not su er from the so called curse of dimensionality and it can be used to solve problems that were out of reach so far. We give some results of convergence and show numerically that it is effective. Besides we numerically show that the new scheme developed can be used to solve some full non linear PDEs. At last we provide an effective algorithm to implement Read more [...]


Option valuation and hedging using asymmetric risk function: asymptotic optimality through fully nonlinear Partial Differential Equations - Emmanuel Gobet, Isaque Pimentel, Xavier Warin

Discrete time hedging produces a residual risk, namely, the tracking error. The major problem is to get valuation/hedging policies minimizing this error. We evaluate the risk between trading dates through a function penalizing asymmetrically profits and losses. After deriving the asymptotics within a discrete time risk measurement for a large number of trading dates, we derive the optimal strategies minimizing the asymptotic risk in the continuous time setting. We characterize the optimality through Read more [...]


Nesting Monte Carlo for high-dimensional Non Linear PDEs - Xavier Warin

A new method based on nesting Monte Carlo is developed to solve highdimensional semi-linear PDEs. Convergence of the method is proved and its convergence rate studied. Results in high dimension for different kind of non-linearities show its efficiency.


Assessing the implementation of the Market Stability Reserve

Corinne Chaton, Anna Creti, and Maria-Eugenia Sanin, Abstract In October 2015 the European Parliament has established a market stability reserve (MSR) in the Phase 4 of the EU-ETS, as part of the 2030 framework for climate policies. In this paper we model the EU-ETS in presence of the Market Stability Reserve (MSR) as it is de ned by that decision and investigate the impact that such a measure has in terms of permits price, output production and banking strategies. To do so we build an inter-temporal Read more [...]


An Adverse Selection Approach to Power Tarification

Clémence Alasseur, Ivar Ekeland, Romuald Élie, Nicolás Hernández Santibáñez and Dylan Possamaï We study the optimal design of electricity contracts among a population of consumers with different needs. This question is tackled within the framework of Principal-Agent problem in presence of adverse selection. The particular features of electricity induce an unusual structure on the production cost, with no decreasing return to scale. We are nevertheless able to provide an explicit solution Read more [...]


StOpt library

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Capacity Expansion Games with Application to Competition in Power Generation Investments

R. Aid, L. Li, M. Ludkovski We consider competitive capacity investment for a duopoly of two distinct producers. The producers are exposed to stochastically uctuating costs and interact through aggregate supply. Capacity expansion is irreversible and modeled in terms of timing strategies characterized through threshold rules. Because the impact of changing costs on the producers is asymmetric, we are led to a nonzerosum timing game describing the transitions among the discrete investment stages. Read more [...]


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 between commodity markets and the stock market. It also shows that speculators and investors both provide and consume liquidity Read more [...]


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 coefficients. A variance reduction method relying on interacting particle systems is also developed. Key words: unbiased estimate, linear parabolic PDEs, interacting Read more [...]

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