Alexandre Popier

A Finite Horizon Optimal Multiple Switching Problem

-1We consider the problem of optimal multiple switching in a finite horizon when the state of the system, including the switching costs, is a general adapted stochastic process. The problem is formulated as an extended impulse control problem and solved using probabilistic tools such as the Snell envelope of processes and reflected backward stochastic differential equations. Finally, when the state of the system is a Markov process, we show that the associated vector of value functions provides a viscosity solution to a system of variational inequalities with interconnected obstacles.

BSDEs with monotone generator driven by Brownian and Poisson noises in a general filtration

We analyze multidimensional BSDEs in a filtration that supports a Brownian motion and a Poisson random measure. Under a monotonicity assumption on the driver, the paper extends several results from the literature. We establish existence and uniqueness of solutions in provided that the generator and the terminal condition satisfy appropriate integrability conditions. The analysis is first carried out under a deterministic time horizon, and then generalized to random time horizons given by a stopping time with respect to the underlying filtration. Moreover, we provide a comparison principle in dimension one.

Optimal Cross Hedging of Insurance Derivatives

Abstract We consider insurance derivatives depending on an external physical risk process, for example, a temperature in a low dimensional climate model. We assume that this process is correlated with a tradable financial asset. We derive optimal strategies for exponential utility from terminal wealth, determine the indifference prices of the derivatives, and interpret them in terms of diversification pressure. Moreover, we check the optimal investment strategies for standard admissibility criteria. Finally, we compare the static risk connected with an insurance derivative to the reduced risk due to a dynamic investment into the correlated asset. We show that dynamic hedging reduces the risk aversion in terms of entropic risk measures by a factor related to the correlation.

Lp-SOLUTIONS FOR REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS

This paper deals with the problem of existence and uniqueness of a solution for a backward stochastic differential equation (BSDE for short) with one reflecting barrier in the case when the terminal value, the generator and the obstacle process are Lp-integrable with p ∈ ]1, 2[. To construct the solution we use two methods: penalization and Snell envelope. As an application we broaden the class of functions for which the related obstacle partial differential equation problem has a unique viscosity solution.

Fractional Diffusion with Partial Observations

This article is devoted to the large sample asymptotic properties of the Maximum Likelihood Estimator (MLE) for the signal drift parameter in a partially observed and possibly controlled fractional diffusion system, perturbed by independent normalized fBms with the same Hurst parameter.

Lp-solution for BSDEs with jumps in the case p<2: Corrections to the paper ‘BSDEs with monotone generator driven by Brownian and Poisson noises in a general filtration’

In [8] we established existence and uniqueness of solutions of backward stochastic differential equations in L^p under a monotonicity condition on the generator and in a general filtration. There was a mistake in the case 1 \textless{} p \textless{} 2. Here we give a corrected proof. Moreover the quasi-left continuity condition on the filtration is removed.In T. Kruse and A. Popier, we established existence and uniqueness of solutions of backward stochastic differential equations in under a monotonicity condition on the generator and in a general filtration. There was a mistake in the case . Here we give a corrected proof. Moreover the quasi-left continuity condition on the filtration is removed.