In this paper, we study the dynamics of contagious spreading processes taking place in complex contact networks. We specifically present a lower-bound on the decay rate of the number of nodes infected by a susceptible-infectedsusceptible (SIS) stochastic spreading process. A precise quantification of this decay rate is crucial for designing efficient strategies to contain epidemic outbreaks. Ho...

The distribution of the present value of a series of cash flows under stochastic interest rates has been investigated by many researchers. One of the main problems in this context is the fact that the calculation of exact analytical results for this type of distributions turns out to be rather complicated, and is known only for special cases. An interesting solution to this difficulty consists ...

This paper examines the relationship between option pricing models that use stochastic dominance concepts in discrete time, and the traditional arbitrage-based continuous time models. It derives multiperiod discrete time index option bounds based on stochastic dominance considerations for a risk-averse investor holding only the underlying asset, the riskless asset and (possibly) the option for ...

We study regularizing effects of nonlinear stochastic perturbations for fully nonlinear PDE. More precisely, path-by-path L bounds for the second derivative of solutions to such PDE are shown. These bounds are expressed as solutions to reflected SDE and are shown to be optimal.

We derive an algorithm in the spirit of Rogers and Davis, Burstein that leads to upper bounds for stochastic control problems. Our bounds complement lower biased estimates recently obtained in Guyon, Henry-Labordere. We evaluate our estimates in two numerical examples motivated from mathematical finance. Joint work with Christian Litterer and Zhenjie Ren. ∗Speaker †Corresponding author: pierre....

A stochastic dynamical system represented through a linear vector equation in idempotent algebra is considered. We propose simple bounds on the mean growth rate of the system state vector, and give an analysis of absolute error of a bound. As an illustration, numerical results of evaluation of the bounds for a test system are also presented.

The (max,+ )-algebra approach is applied to establish some monotonicity properties and to get algebraic bounds on the service cycle completion times in acyclic fork-join queueing networks. The obtained results are extended to derive simple lower and upper bounds on the mean cycle time in stochastic networks.

Simple lower and upper bounds on mean cycle time in stochastic acyclic fork-join networks are derived using the (max,+)-algebra approach. The behaviour of the bounds under various assumptions concerning the service times in the networks is discussed, and related numerical examples are presented.

We establish novel moment bounds for strong solutions of the stochastic 3D Primitive Equations. Using these bounds we establish the continuity of the associated Markovian semigroup and prove the existence of an invariant measure associated to these equations. This measure is supported on strong solutions, but is furthermore shown to have higher regularity properties.

Risk-averse multistage stochastic programs appear in multiple areas and are challenging to solve. Stochastic Dual Dynamic Programming (SDDP) is a well-known tool address such problems under time-independence assumptions. We show how derive dual formulation for these apply an SDDP algorithm, leading converging deterministic upper bounds risk-averse problems.