Stochastic target problems with controlled loss in jump diffusion models

In this paper, we consider a mixed diffusion version of the stochastic target problem introduced by Bouchard et al. (2009). This consists in finding the minimum initial value of a controlled process which guarantees to reach a controlled stochastic target with a given lovel of expected loss. As in Bouchard et al. (2009), it can be converted into a standard stochastic target problem, as already studied by Soner and Touzi (2002) or Bouchard (2002) for the mixed diffusion case, by increasing both the state space and the dimension of the control. In our mixed-diffusion setting, the main difficulty comes from the presence of jumps, which leads to the introduction of a new kind of controls that take values in an unbounded set of measurable maps. This has non trivial impacts on the formulation and derivation of the associated partial differential equations.stochastic target problem; mixed diffusion process; discontinuous viscosity solutions; quantile hedging

Analysis of micro-seismicity in sea ice with deep learning and Bayesian inference: application to high-resolution thickness monitoring

In the perspective of upcoming seasonally ice-free Arctic, understanding the dynamics of sea ice in the changing climate is a major challenge in oceanography and climatology. In particular, the new generation of sea ice models will require fine parameterization of sea ice thickness and rheology. With the rapidly evolving state of sea ice, achieving better accuracy, as well as finer temporal and spatial resolutions of its thickness will set new monitoring standards, with major scientific and geopolitical implications. Recent studies have shown the potential of passive seismology to monitor the thickness, density and elastic properties of sea ice with significantly reduced logistical constraints. For example, human intervention is no longer required, except to install and uninstall the geophones. Building up on this approach, we introduce a methodology for estimating sea ice thickness with high spatial and temporal resolutions from the analysis of icequakes waveforms. This methodology is based on a deep convolutional neural network for automatic clustering of the ambient seismicity recorded on sea ice, combined with a Bayesian inversion of the clustered waveforms. By applying this approach to seismic data recorded in March 2019 on fast ice in the Van Mijen fjord (Svalbard), we observe the spatial clustering of icequakes sources along the shore line of the fjord. The ice thickness is shown to follow an increasing trend that is consistent with the evolution of temperatures during the four weeks of data recording. Comparing the energy of the icequakes with that of calibrated seismic sources, we were able to derive a power law of icequake energy, and to relate this energy to the size of the cracks that generate the icequakes.</p

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

Abstract 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

Sea ice thickness and elastic properties from the analysis of multimodal guided wave propagation measured with a passive seismic array

Field data are needed for a better understanding of sea ice decline in the context of climate change. The rapid technological and methodological advances of the last decade have led to a reconsideration of seismic methods in this matter. In particular, passive seismology has filled an important gap by removing the need to use active sources. We present a seismic experiment where an array of 247 geophones was deployed on sea ice, in the Van Mijen fjord near Sveagruva (Svalbard). The array is a mix of 1C and 3C stations with sampling frequencies of 500 and 1000 Hz. They recorded continuously the ambient seismic field in sea ice between 28 February and 26 March 2019. Data also include active acquisitions on 1 and 26 March with a radar antenna, a shaker unit, impulsive sources, and artificial sources of seismic noise. This data set is of unprecedented quality regarding sea ice seismic monitoring, as it also includes thousands of microseismic events recorded each day. By combining passive seismology approaches with specific array processing methods, we demonstrate that the multimodal dispersion curves of sea ice can be calculated without an active source and then used to infer sea ice properties. We calculated an ice thickness, Young's modulus, and Poisson's ratio with values h=543 cm, E=3.90.15 GPa, and nu=0.340.02 on 1 March, and h=583 cm, E=4.4 +/- 0.15 GPa, and nu=0.32 +/- 0.02 on 5 March. These values are consistent with in situ field measurements and observations.Peer reviewe