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Solving Nonlinear and High-Dimensional Partial Differential Equations via Deep Learning
TLDR
We apply the Deep Galerkin Method (DGM) described in Sirignano and Spiliopoulos (2018) to solve a number of partial differential equations that arise in quantitative finance applications including option pricing, optimal execution, mean field games, etc. Expand
Stochastic Control and Differential Games with Path-Dependent Influence of Controls on Dynamics and Running Cost
  • Yuri F. Saporito
  • Mathematics, Computer Science
  • SIAM J. Control. Optim.
  • 2 November 2016
TLDR
We use the functional Ito calculus framework to find a path-dependent version of the Hamilton--Jacobi-Bellman equation for stochastic control problems that feature dynamics and running costs that depend on the path of the control. Expand
Functional Ito Calculus, Path-dependence and the Computation of Greeks
Dupire's functional It\^o calculus provides an alternative approach to the classical Malliavin calculus for the computation of sensitivities, also called Greeks, of path-dependent derivatives prices.Expand
Multiscale Stochastic Volatility Model For Derivatives On Futures
In this paper, we present a new method for computing the first-order approximation of the price of derivatives on futures in the context of multiscale stochastic volatility studied in Fouque et al.Expand
The functional Meyer–Tanaka formula
TLDR
The functional Ito formula, firstly introduced by Bruno Dupire for continuous semimartingales, might be extended in two directions: different dynamics for the underlying process and/or weaker assumptions on the regularity of the functional. Expand
Applications of the Deep Galerkin Method to Solving Partial Integro-Differential and Hamilton-Jacobi-Bellman Equations
We extend the Deep Galerkin Method (DGM) introduced in Sirignano and Spiliopoulos (2018) to solve a number of partial differential equations (PDEs) that arise in the context of optimal stochasticExpand
Stochastic control and differential games with path-dependent controls
In this paper we consider the functional Ito calculus framework to find a path-dependent version of the Hamilton-Jacobi-Bellman equation for stochastic control problems with path-dependence in theExpand
FIRST-ORDER ASYMPTOTICS OF PATH-DEPENDENT DERIVATIVES IN MULTISCALE STOCHASTIC VOLATILITY ENVIRONMENT
In this paper, we extend the first-order asymptotics analysis of Fouque et al. to general path-dependent financial derivatives using Dupire's functional Ito calculus. The main conclusion is that theExpand
The calibration of stochastic local-volatility models: An inverse problem perspective
TLDR
We tackle the calibration of the so-called Stochastic-Local Volatility (SLV) model, a class of financial models that combines the local and stochastic volatility features. Expand
Stochastic Control with Delayed Information and Related Nonlinear Master Equation
TLDR
We study stochastic control problems with delayed information, that is, the control at time $T$ can depend only on the information observed before time $t-H$ for some delay parameter $H$. Expand
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