A framework for adaptive Monte-Carlo procedures

Adaptive Monte Carlo methods are recent variance reduction techniques. In this work, we propose a mathematical setting which greatly relaxes the assumptions needed by for the adaptive importance sampling techniques presented by Vazquez-Abad and Dufresne, Fu and Su, and Arouna. We establish the convergence and asymptotic normality of the adaptive Monte Carlo estimator under local assumptions which are easily verifiable in practice. We present one way of approximating the optimal importance sampling parameter using a randomly truncated stochastic algorithm. Finally, we apply this technique to some examples of valuation of financial derivatives

American Options Based on Malliavin Calculus and Nonparametric Variance Reduction Methods

This paper is devoted to pricing American options using Monte Carlo and the Malliavin calculus. Unlike the majority of articles related to this topic, in this work we will not use localization fonctions to reduce the variance. Our method is based on expressing the conditional expectation E[f(St)/Ss] using the Malliavin calculus without localization. Then the variance of the estimator of E[f(St)/Ss] is reduced using closed formulas, techniques based on a conditioning and a judicious choice of the number of simulated paths. Finally, we perform the stopping times version of the dynamic programming algorithm to decrease the bias. On the one hand, we will develop the Malliavin calculus tools for exponential multi-dimensional diffusions that have deterministic and no constant coefficients. On the other hand, we will detail various nonparametric technics to reduce the variance. Moreover, we will test the numerical efficiency of our method on a heterogeneous CPU/GPU multi-core machine

Convenient Multiple Directions of Stratification

This paper investigates the use of multiple directions of stratification as a variance reduction technique for Monte Carlo simulations of path-dependent options driven by Gaussian vectors. The precision of the method depends on the choice of the directions of stratification and the allocation rule within each strata. Several choices have been proposed but, even if they provide variance reduction, their implementation is computationally intensive and not applicable to realistic payoffs, in particular not to Asian options with barrier. Moreover, all these previously published methods employ orthogonal directions for multiple stratification. In this work we investigate the use of algorithms producing convenient directions, generally non-orthogonal, combining a lower computational cost with a comparable variance reduction. In addition, we study the accuracy of optimal allocation in terms of variance reduction compared to the Latin Hypercube Sampling. We consider the directions obtained by the Linear Transformation and the Principal Component Analysis. We introduce a new procedure based on the Linear Approximation of the explained variance of the payoff using the law of total variance. In addition, we exhibit a novel algorithm that permits to correctly generate normal vectors stratified along non-orthogonal directions. Finally, we illustrate the efficiency of these algorithms in the computation of the price of different path-dependent options with and without barriers in the Black-Scholes and in the Cox-Ingersoll-Ross markets.Comment: 21 pages, 11 table

A laboratory method to evaluate the sensitivity of Colletotrichum musea to post harvest fungicides

Introduction. Ce protocole vise à détecter et évaluer des variations de sensibilité dans des populations de Colletotrichum musae vis-à-vis des fongicides actuellement utilisés pour le contrôle des maladies de conservation des bananes. Le principe, les principaux avantages, le matériel végétal de départ, le temps nécessaire et les résultats attendus de la méthode sont présentés. Matériel et méthodes. Le matériel de laboratoire nécessaire, et le détail des douze étapes du protocole réalisé pour l'échantillonnage des bananes et le développement des lésions dues à l'anthracnose, la préparation des boites de milieu gélosé (agar), les isolements monospores, les tests de germination et l'analyse des données sont décrits. De possibles problèmes sont évoqués. Nous obtenons (a) pour les produits antimitotiques, le pourcentage de souches résistantes dans la population analysée ; (b) pour des fongicides inhibiteurs de la biosynthèse des stérols (SBI), la variation et la distribution de la sensibilité des isolats dans la population analysée en fonction de la réduction de leur croissance radiale, imputable au fongicide. (Résumé d'auteur

A laboratory method to evaluate Pseudocercospora musae (teleomorph: Mycosphaerella musicola) sensitivity to fungicides

Introduction. Le protocole vise à détecter et évaluer des variations de sensibilité dans des populations de Pseudocercospora musae (téléomorphe : Mycosphaerella musicola) vis à vis de fongicides qui sont utilisés pour contrôler la maladie de Sigatoka chez le bananier. Le principe, les principaux avantages, le matériel végétal de départ, le temps nécessaire et les résultats attendus de la méthode sont présentés. Matériel et méthodes. Le matériel de laboratoire nécessaire et le détail des sept étapes du protocole réalisées sur quatre jours d'expérimentation sont décrits. Résultats. Le protocole aboutit à l'observation de la germination de conidies (aspect ou croissance du tube germinatif) de P. musae selon la sensibilité aux fongicides. (Résumé d'auteur

Wall slip across the jamming transition of soft thermoresponsive particles

Flows of suspensions are often affected by wall slip, that is the fluid velocity $v_{f}$ in the vicinity of a boundary differs from the wall velocity $v_{w}$ due to the presence of a lubrication layer. While the slip velocity $v_s=\vert v_{f}-v_{w}\vert$ robustly scales linearly with the stress $\sigma$ at the wall in dilute suspensions, there is no consensus regarding denser suspensions that are sheared in the bulk, for which slip velocities have been reported to scale as a $v_s\propto\sigma^p$ with exponents $p$ inconsistently ranging between 0 and 2. Here we focus on a suspension of soft thermoresponsive particles and show that $v_s$ actually scales as a power law of the viscous stress $\sigma-\sigma_c$, where $\sigma_c$ denotes the yield stress of the bulk material. By tuning the temperature across the jamming transition, we further demonstrate that this scaling holds true over a large range of packing fractions $\phi$ on both sides of the jamming point and that the exponent $p$ increases continuously with $\phi$, from $p=1$ in the case of dilute suspensions to $p=2$ for jammed assemblies. These results allow us to successfully revisit inconsistent data from the literature and paves the way for a continuous description of wall slip above and below jamming.Comment: 6 pages, 4 figures - accepted for publication as a Rapid Communication in Phys. Rev.