Loss-Based Risk Measures

Starting from the requirement that risk measures of financial portfolios should be based on their losses, not their gains, we define the notion of loss-based risk measure and study the properties of this class of risk measures. We characterize loss-based risk measures by a representation theorem and give examples of such risk measures. We then discuss the statistical robustness of estimators of loss-based risk measures: we provide a general criterion for qualitative robustness of risk estimators and compare this criterion with sensitivity analysis of estimators based on influence functions. Finally, we provide examples of statistically robust estimators for loss-based risk measures.Comment: 40 page

Sensitivity analysis in HMMs with application to likelihood maximization

International audienceThis paper considers a sensitivity analysis in Hidden Markov Models with continuous state and observation spaces. We propose an Infinitesimal Perturbation Analysis (IPA) on the filtering distribution with respect to some parameters of the model. We describe a methodology for using any algorithm that estimates the filtering density, such as Sequential Monte Carlo methods, to design an algorithm that estimates its gradient. The resulting IPA estimator is proven to be asymptotically unbiased, consistent and has computational complexity linear in the number of particles. We consider an application of this analysis to the problem of identifying unknown parameters of the model given a sequence of observations. We derive an IPA estimator for the gradient of the log-likelihood, which may be used in a gradient method for the purpose of likelihood maximization. We illustrate the method with several numerical experiments

Particle filter-based policy gradient for pomdps

International audienceOur setting is a Partially Observable Markov Decision Process with continuous state, observation and action spaces. Decisions are based on a Particle Filter for estimating the belief state given past observations. We consider a policy gradient approach for parameterized policy optimization. For that purpose, we investigate sensitivity analysis of the performance measure with respect to the parameters of the policy, focusing on Finite Difference (FD) techniques. We show that the naive FD is subject to variance explosion because of the non-smoothness of the resampling procedure. We propose a more sophisticated FD method which overcomes this problem and establish its consistency

Numerical methods for sensitivity analysis of Feynman-Kac models

The aim of this work is to provide efficient numerical methods to estimate the gradient of a Feynman-Kac flow with respect to a parameter of the model. The underlying idea is to view a Feynman-Kac flow as an expectation of a product of potential functions along a canonical Markov chain, and to use usual techniques of gradient estimation in Markov chains. Combining this idea with the use of interacting particle methods enables us to obtain two new algorithms that provide tight estimations of the sensitivity of a Feynman-Kac flow. Each algorithm has a linear computational complexity in the number of particles and is demonstrated to be asymptotically consistent. We also carefully analyze the differences between these new algorithms and existing ones. We provide numerical experiments to assess the practical efficiency of the proposed methods and explain how to use them to solve a parameter estimation problem in Hidden Markov Models. To conclude we can say that these algorithms outperform the existing ones in terms of trade-off between computational complexity and estimation quality

Incertitude de modèle en finance (mesures de risque et calibration de modèles)

PALAISEAU-Polytechnique (914772301) / SudocSudocFranceF

One-Pot Synthesis of 2,3-Dihydro-pyrrolopyridinones Using in Situ Generated Formimines

International audienceA novel one-pot methodology is described for the synthesis of functionalized pyrrolopyridinones using in situ generated formimines and an ortho-lithiated pyridinecarboxamide species. Depending on the reaction conditions, this procedure allows versatile access to aminomethylated pyridinecarboxamides, 2,3-dihydro-pyrrolopyridinones, or 1,1-dialkylated 2,3-dihydro-pyrrolopyridinone derivatives