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6 papers · 2 filters
Lyapunov conditions for logarithmic Sobolev and Super Poincaré inequality
Patrick Cattiaux, Arnaud Guillin, Feng-Yu Wang +1
We show how to use Lyapunov functions to obtain functional inequalities which are stronger than Poincaré inequality (for instance logarithmic Sobolev or -Sobolev). The case of P…
A large deviation approach to optimal transport
Christian Léonard
A probabilistic method for solving the Monge-Kantorovich mass transport problem on is introduced. A system of empirical measures of independent particles is built in such a w…
Pricing, Hedging and Optimally Designing Derivatives Via Minimization of Risk Measures
Pauline Barrieu, Nicole El Karoui
The question of pricing and hedging a given contingent claim has a unique solution in a complete market framework. When some incompleteness is introduced, the problem becomes howev…
Nonlinear SDEs driven by Lévy processes and related PDEs
Benjamin Jourdain, Sylvie Méléard, Wojbor Woyczynski
In this paper we study general nonlinear stochastic differential equations, where the usual Brownian motion is replaced by a Lévy process. We also suppose that the coefficient mult…
Rate of Converrgence for ergodic continuous Markov processes : Lyapunov versus Poincare
Dominique Bakry, Patrick Cattiaux, Arnaud Guillin
We study the relationship between two classical approaches for quantitative ergodic properties : the first one based on Lyapunov type controls and popularized by Meyn and Tweedie,…
Bid-Ask Dynamic Pricing in Financial Markets with Transaction Costs and Liquidity Risk
Jocelyne Bion-Nadal
We introduce, in continuous time, an axiomatic approach to assign to any financial position a dynamic ask (resp. bid) price process. Taking into account both transaction costs and…