arXiv subjects

Ludovic Moreau

Publications and source records attributed to Ludovic Moreau.

8 recordsLinked to original sources

arXiv2026

Optimal Control with Expectation Constraint in a Smooth Boundary Case

As in Bouchard et al. (2010) and Bouchard and Nutz (2014), we study a utility maximization problem with expectation constraint. We first consider a uniformly elliptic case in which the endogenous state boundary associated with the constraint in expectation is proved to be smooth. This allows one to derive a proper Dirichlet condition for the value function of the optimal control problem on this boundary. We then propose a new truncation argument in the martingale representation of the expectation constraint. This leads to an approximating sequence of auxiliary systems of PDEs for which comparison holds. Convergence to the initial optimal control problem is proved. In the degenerate case, we propose another approximation which consists in adding a small noise term to recover uniformly ellipticity. Convergence is also proved. To the best of our knowledge, it is the first time that a full analysis is performed for such control problems, so as to open the doors to the use of numerical schemes. Numerical resolution in a toy example is performed using neural networks. It is complemented by an estimation of the numerical error, also performed by using a neural network approach.

math.OC↗

arXiv2026

High-resolution measurement of sea ice mechanical characteristics using Distributed Acoustic Sensing

Sea ice mechanical properties are involved in dynamical processes acting from the scale of meters to several hundred kilometers. The current rapid changes in the state of polar sea ice require a better understanding and modeling of these processes and, therefore, accurate measurements of properties including sea ice thickness, density, Young's modulus and Poisson's ratio. These properties can be measured by tracking the propagation of elastic waves within the ice. Recent technological advances have enabled the use of fiber-optic cables as cost-effective, dense seismic arrays. Once connected to an interrogator unit and mechanically coupled to a medium, here the ice cover, these cables can monitor strain field propagation, using a technique called Distributed Acoustic Sensing (DAS). In this work, we describe the use of such an array of sensors in the coastal ice of the St. Lawrence Estuary, Canada, where a 600 m long optical fiber was deployed across three different morphological sea ice conditions. During hour-long recordings, we measured the propagation of both multi-modal seismic signals generated by active sources and hydro-elastic swell. We computed dispersion curves of active signals and used Continuous Wavelet Transform (CWT) to observe the evolution of swell characteristics in the different ice areas. The dispersion curves were successfully inverted to measure the spatial evolution of ice thickness, and Young's and flexural rigidity in each of these areas. We observed ice thicknesses from 25 cm to 68 cm and Young's modulus values between 4.5 GPa and 5.7 GPa, in good agreement with values derived from collocated geophone arrays and drill hole thickness measurements. DAS systems therefore appear to be effective in evaluating heterogeneous sea ice mechanical properties and thus sea ice formation history and dynamics.

physics.geo-ph↗

arXiv2021

Ultrasonic monitoring of stress and cracks of the 1/3 scale mock-up of nuclear reactor concrete containment structure

To evaluate the stress level and damage of a reinforced concrete containment wall and its reaction to pressure variations, we implemented successive ultrasonic experiments on the exterior surface of the containment wall in the gusset area for three consecutive years. During each experiment, the pressure inside the containment wall increased gradually from 0 MPa to 0.43 MPa and then decreased back to 0 Mpa.From the analysis of the ultrasonic coda waves obtained in the multiple scattering regime, we performed Coda Wave Interferometry to calculate the apparent velocity changes in the structure (denoted by $dV/V_a$) and Coda Wave Decorrelation (DC) measurements to produce 3D cartographies of stress and crack distribution. From three source-receiver pairs, located at the top, middle and bottom of the experimental region, we observe that coda waves dilate, shrink and remain almost unchanged, respectively. This corresponds to the decreasing, increasing and invariant pressure inside the concrete. The comparison of three years' results demonstrates that the variation of $dV/V_a$ and DC under the same pressure test increases through the years, which indicates the progressive deterioration and aging of the concrete. From a large collection of source-receiver pairs at different times, the spatial-temporal variations of $dV/V_a$ and DC are then used to produce a map of the structural velocity and scattering changes, respectively. We observe a decreasing velocity on the top part and an increasing in the middle one, which is in line with the $dV/V_a$ analysis. The reconstructed scattering changes (or structural changes) highlight the active region during the inflation-deflation procedure, corresponding to the opening and closing (and sometimes the development) of cracks. The larger magnitude in 2019 than in 2017 indicates the increasing damage in the concrete.

cond-mat.mtrl-sci↗

arXiv2018

On a class of path-dependent singular stochastic control problems

This paper studies a class of non$-$Markovian singular stochastic control problems, for which we provide a novel probabilistic representation. The solution of such control problem is proved to identify with the solution of a $Z-$constrained BSDE, with dynamics associated to a non singular underlying forward process. Due to the non$-$Markovian environment, our main argumentation relies on the use of comparison arguments for path dependent PDEs. Our representation allows in particular to quantify the regularity of the solution to the singular stochastic control problem in terms of the space and time initial data. Our framework also extends to the consideration of degenerate diffusions, leading to the representation of the solution as the infimum of solutions to $Z-$constrained BSDEs. As an application, we study the utility maximisation problem with transaction costs for non$-$Markovian dynamics.

math.OC↗

arXiv2015

Trading with Small Price Impact

An investor trades a safe and several risky assets with linear price impact to maximize expected utility from terminal wealth. In the limit for small impact costs, we explicitly determine the optimal policy and welfare, in a general Markovian setting allowing for stochastic market, cost, and preference parameters. These results shed light on the general structure of the problem at hand, and also unveil close connections to optimal execution problems and to other market frictions such as proportional and fixed transaction costs.

q-fin.PM↗

arXiv2014

Regularity of BSDEs with a convex constraint on the gains-process

We consider the minimal super-solution of a backward stochastic differential equation with constraint on the gains-process. The terminal condition is given by a function of the terminal value of a forward stochastic differential equation. Under boundedness assumptions on the coefficients, we show that the first component of the solution is Lipschitz in space and 1/2-Hölder in time with respect to the initial data of the forward process. Its path is continuous before the time horizon at which its left-limit is given by a face-lifted version of its natural boundary condition. This first component is actually equal to its own face-lift. We only use probabilistic arguments. In particular, our results can be extended to certain non-Markovian settings.

math.PR↗

arXiv2014

Hedging under an expected loss constraint with small transaction costs

We consider the problem of option hedging in a market with proportional transaction costs. Since super-replication is very costly in such markets, we replace perfect hedging with an expected loss constraint. Asymptotic analysis for small transactions is used to obtain a tractable model. A general expansion theory is developed using the dynamic programming approach. Explicit formulae are also obtained in the special cases of an exponential or power loss function. As a corollary, we retrieve the asymptotics for the exponential utility indifference price.

q-fin.PM↗

arXiv2014

Stochastic target games with controlled loss

We study a stochastic game where one player tries to find a strategy such that the state process reaches a target of controlled-loss-type, no matter which action is chosen by the other player. We provide, in a general setup, a relaxed geometric dynamic programming principle for this problem and derive, for the case of a controlled SDE, the corresponding dynamic programming equation in the sense of viscosity solutions. As an example, we consider a problem of partial hedging under Knightian uncertainty.

math.OC↗