A deep solver for BSDEs with jumps
Abstract
Picarelli's presentation proposes an innovative extension of the deep solver by Jiequn Han, Arnulf Jentzen, and Weinan E (2018) to tackle forward backward stochastic differential equations (FBSDEs) with jumps. Utilizing a discretized version of FBSDE and employing a family of artificial neural networks (ANNs) to parametrize high-dimensional control processes, Picarelli treats the FBSDE as a model-based reinforcement learning problem. The ANN parameters are optimized under her guidance to minimize a predefined loss function. This approach accommodates both finite and infinite jump activity, introducing an approximation with finitely many jumps for the latter case. Successfully applying the algorithm to option pricing challenges in both low and high dimensions, Picarelli demonstrates its versatility and explores its potential in addressing counterparty credit risk within this context.
Watch recording ↗About the speaker
Athena Picarelli is a Full Professor at the Department of Economics at the University of Verona. She earned her PhD in Applied Mathematics from ENSTA ParisTech (École Nationale Supérieure de Techniques Avancées) in Paris. She then completed a two-year postdoctoral fellowship at the University of Oxford (Nomura Fellowship) and a one-year postdoctoral position at Imperial College London (CFM Fellowship). She joined the University of Verona in 2018. Her research interests include stochastic optimal control, Hamilton-Jacobi-Bellman equations, numerical methods for partial differential equations, and computational finance