Related papers: Deep Signature Algorithm for Multi-dimensional Pat…
In this paper, we aim to solve the high dimensional stochastic optimal control problem from the view of the stochastic maximum principle via deep learning. By introducing the extended Hamiltonian system which is essentially an FBSDE with a…
In this paper, we present a scalable deep learning approach to solve opinion dynamics stochastic optimal control problems with mean field term coupling in the dynamics and cost function. Our approach relies on the probabilistic…
Deep unfolding neural networks derived from iterative optimization schemes and numerical ordinary/partial differential equations (ODEs/PDEs) have attracted much attention in data science over the last decade. Therein, numerous important…
This paper studies how to price and hedge options under stock models given as a path-dependent SDE solution. When the path-dependent SDE coefficients have Fr\'{e}chet derivatives, an option price is differentiable with respect to time and…
This paper is dedicated to the presentation and the analysis of a numerical scheme for forward-backward SDEs of the McKean-Vlasov type, or equivalently for solutions to PDEs on the Wasserstein space. Because of the mean field structure of…
We propose a new probabilistic scheme which combines deep learning techniques with high order schemes for backward stochastic differential equations belonging to the class of Runge-Kutta methods to solve high-dimensional semi-linear…
In this article we introduce a portfolio optimisation framework, in which the use of rough path signatures (Lyons, 1998) provides a novel method of incorporating path-dependencies in the joint signal-asset dynamics, naturally extending…
This paper presents a multinomial method for option pricing when the underlying asset follows an exponential Variance Gamma process. The continuous time Variance Gamma process is approximated by a discrete time Markov chain with the same…
Hedging exotic options in presence of market frictions is an important risk management task. Deep hedging can solve such hedging problems by training neural network policies in realistic simulated markets. Training these neural networks may…
The Black-Scholes option pricing model remains a cornerstone in financial mathematics, yet its application is often challenged by the need for accurate hedging strategies, especially in dynamic market environments. This paper presents a…
Multi-asset option pricing under local- and stochastic-volatility models leads naturally to high-dimensional parabolic PDEs. We develop an end-to-end quantum PDE framework for European option pricing under local-volatility Black--Scholes…
An American option grants the holder the right to select the time at which to exercise the option, so pricing an American option entails solving an optimal stopping problem. Difficulties in applying standard numerical methods to complex…
We develop an unsupervised deep learning method to solve the barrier options under the Bergomi model. The neural networks serve as the approximate option surfaces and are trained to satisfy the PDE as well as the boundary conditions. Two…
We define a class of reflected backward stochastic differential equation (RBSDE) driven by a marked point process (MPP) and a Brownian motion, where the solution is constrained to stay above a given c\`adl\`ag process. The MPP is only…
This paper presents machine learning techniques and deep reinforcement learningbased algorithms for the efficient resolution of nonlinear partial differential equations and dynamic optimization problems arising in investment decisions and…
In this work, in order to obtain higher-order schemes for solving forward backward stochastic differential equations, we adopt the high-order multi-step method in [W. Zhao, Y. Fu and T. Zhou, SIAM J. Sci. Comput., 36(4) (2014),…
The interface between stochastic analysis and machine learning is a rapidly evolving field, with path signatures - iterated integrals that provide faithful, hierarchical representations of paths - offering a principled and universal feature…
This paper is dedicated to solving high-dimensional coupled FBSDEs with non-Lipschitz diffusion coefficients numerically. Under mild conditions, we provided a posterior estimate of the numerical solution that holds for any time duration.…
We propose a numerical method for solving high dimensional fully nonlinear partial differential equations (PDEs). Our algorithm estimates simultaneously by backward time induction the solution and its gradient by multi-layer neural…
In this paper, we consider a class of backward doubly stochastic differential equations (BDSDE for short) with general terminal value and general random generator. Those BDSDEs do not involve any forward diffusion processes. By using the…