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On the rate of convergence of finite-difference approximations for Bellman equations with Lipschitz coefficients
TLDR
In this paper, the authors considered parabolic Bellman equations with Lipschitz coefficients and obtained error bounds of order $h 1/2$ for certain types of finite-difference schemes.Abstract:
We consider parabolic Bellman equations with Lipschitz coefficients. Error bounds of order $h^{1/2}$ for certain types of finite-difference schemes are obtained.read more
Citations
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Journal ArticleDOI
A rate of convergence for monotone finite difference approximations to fully nonlinear, uniformly elliptic PDEs
TL;DR: In this article, the authors obtained an algebraic rate of convergence for monotone and consistent finite difference approximations to Lipschitz-continuous viscosity solutions of uniformly elliptic partial differential equations.
Journal ArticleDOI
Error estimates for approximate solutions to Bellman equations associated with controlled jump-diffusions
TL;DR: In this article, error bounds for a class of monotone approximation schemes, which under some assumptions includes finite difference schemes, and bounds on the error induced when the original Levy measure is replaced by a finite measure with compact support, are derived.
Posted Content
A model-free no-arbitrage price bound for variance options
J. Frédéric Bonnans,Xiaolu Tan +1 more
TL;DR: In this article, the authors consider the model-free no-arbitrage bound of variance option given the marginal distributions of the underlying asset and propose a gradient projection algorithm together with a finite difference scheme to approximate the bound.
DissertationDOI
Discretisation of continuous-time stochastic optimal control problems with delay
TL;DR: In this article, the authors studied discretisation schemes for continuous-time stochastic optimal control problems with time delay, where the dynamics of the control problems to be approximated are described by controlled stochastically delay (or functional) differential equations and the value functions associated with such control problems are defined on an infinite-dimensional function space.
Option pricing with short selling restrictions or bans being imposed
TL;DR: Guo et al. as discussed by the authors proposed a new partial differential equation (PDE) approach to price European call options under the hard-to-borrow stock model and then an alternative direction implicit (ADI) scheme was applied to solve it numerically.
References
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Book
Controlled Markov processes and viscosity solutions
Wendell H. Fleming,H. Mete Soner +1 more
TL;DR: In this paper, an introduction to optimal stochastic control for continuous time Markov processes and to the theory of viscosity solutions is given, as well as a concise introduction to two-controller, zero-sum differential games.
Book
Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations
TL;DR: In this paper, the main ideas on a model problem with continuous viscosity solutions of Hamilton-Jacobi equations are discussed. But the main idea of the main solutions is not discussed.
Book
Numerical Methods for Stochastic Control Problems in Continuous Time
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
On the convergence rate of approximation schemes for Hamilton-Jacobi-Bellman equations
Guy Barles,Espen R. Jakobsen +1 more
TL;DR: General results on the rate of convergence of a certain class of monotone approximation schemes for stationary Hamilton-Jacobi- Bellman equations with variable coecients are obtained using systematically a tricky idea of N.V. Krylov.
Journal ArticleDOI
Error Bounds for Monotone Approximation Schemes for Hamilton-Jacobi-Bellman Equations
Guy Barles,Espen R. Jakobsen +1 more
TL;DR: The key step in the proof of these new estimates is the introduction of a switching system which allows the construction of approximate, (almost) smooth supersolutions for the Hamilton--Jacobi--Bellman equation.