Nonlinear integro-differential evolution problems arising in option pricing: a viscosity solutions approach

Continuous Dependence Estimates for Viscosity Solutions of Integro-pdes

We present a general framework for deriving continuous dependence estimates for, possibly polynomially growing, viscosity solutions of fully nonlinear degenerate parabolic integro-PDEs. We use this framework to provide explicit estimates for the continuous dependence on the coefficients and the “Lévy measure” in the Bellman/Isaacs integro-PDEs arising in stochastic control/differential games. M...

Obstacle Problem for Nonlinear Integro{differential Equations Arising in Option Pricing

Approximate solution of system of nonlinear Volterra integro-differential equations by using Bernstein collocation method

This paper presents a numerical matrix method based on Bernstein polynomials (BPs) for approximate the solution of a system of m-th order nonlinear Volterra integro-differential equations under initial conditions. The approach is based on operational matrices of BPs. Using the collocation points,this approach reduces the systems of Volterra integro-differential equations associated with the giv...

Integro-differential equations for option prices in exponential Lévy models

We explore the precise link between option prices in exponential Lévy models and the related partial integro-differential equations (PIDEs) in the case of European options and options with single or double barriers. We first discuss the conditions under which options prices are classical solutions of the PIDEs. We show that these conditions may fail in pure jump models and give examples of lack...

Inexact Arithmetic Considerations for Direct Control and Penalty

5 Solutions of Hamilton Jacobi Bellman (HJB) Partial Integro Differential Equations (PIDEs) 6 arising in financial option problems are not necessarily unique. In order to ensure conver7 gence of a numerical scheme to the viscosity solution, it is common to use a positive coefficient 8 discretization for such PIDEs. However in finite precision arithmetic one often encounters dif9 ficulties in so...