Proceedings ArticleDOI
Convergence of approximation schemes for fully nonlinear second order equations
Guy Barles,Panagiotis E. Souganidis +1 more
- pp 2347-2349
TLDR
In this article, the convergence of a wide class of approximation schemes to the viscosity solution of fully nonlinear second-order elliptic or parabolic, possibly degenerate, partial differential equations is studied.Abstract:
The convergence of a wide class of approximation schemes to the viscosity solution of fully nonlinear second-order elliptic or parabolic, possibly degenerate, partial differential equations is studied It is proved that any monotone, stable, and consistent scheme converges (to the correct solution), provided that there exists a comparison principle for the limiting equation Several examples are given where the result applies >read more
Citations
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European option pricing with transaction costs
TL;DR: In this article, the authors consider the problem of pricing European options in a market model similar to the Black-Scholes one, except that proportional transaction charges are levied on all sales and purchases.
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Shape From Shading
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TL;DR: This chapter describes the main difficulties of the Shape From Shading problem and the most recent theoretical results and gives some examples of realistic modeling and of rigorous numerical methods.
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A Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential Lévy Models
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Variable Resolution Discretization in Optimal Control
Rémi Munos,Andrew W. Moore +1 more
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Controlled diffusion processes
TL;DR: In this article, the authors give an overview of the developments in controlled diffusion processes, emphasizing key results regarding existence of optimal controls and their characterization via dynamic programming for a variety of cost criteria and structural assumptions.
References
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Book
Elliptic Partial Differential Equations of Second Order
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TL;DR: In this article, Leray-Schauder and Harnack this article considered the Dirichlet Problem for Poisson's Equation and showed that it is a special case of Divergence Form Operators.
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Viscosity solutions of Hamilton-Jacobi equations
TL;DR: In this article, the authors examined viscosity solutions of Hamilton-Jacobi equations, and proved the existence assertions by expanding on the arguments in the introduction concerning the relationship of the vanishing-viscosity method and the notion of viscoity solutions.
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TL;DR: In this paper, a Markov chain is used to approximate the solution of the optimal stochastic control problem for diffusion, reflected diffusion, or jump-diffusion models, and a general method for obtaining a useful approximation is given.
Journal ArticleDOI
Some Properties of Viscosity Solutions of Hamilton-Jacobi Equations.
TL;DR: In this paper, the authors introduced the notion of "viscosity solutions" of scalar nonlinear first order partial differential equations and proved several new facts and reproved various known results in a simpler manner.