An adaptive extrapolation discontinuous Galerkin method for the valuation of Asian options

Authors:
Michael D. Marcozzi
Affiliations:
-
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

Citing 10
Cited 0

Quasimonotone schemes for scalar conservation laws. part 1

SIAM Journal on Numerical Analysis
Parallel, adaptive finite element methods for conservation laws

Proceedings of the third ARO workshop on Adaptive methods for partial differential equations
A Posteriori Finite Element Error Estimation for Diffusion Problems

SIAM Journal on Scientific Computing
Scientific Computing with Ordinary Differential Equations

Scientific Computing with Ordinary Differential Equations
On the Approximation of Optimal Stopping Problems with Application to Financial Mathematics

SIAM Journal on Scientific Computing
Far Field Boundary Conditions for Black--Scholes Equations

SIAM Journal on Numerical Analysis
On the Valuation of Asian Options by Variational Methods

SIAM Journal on Scientific Computing
Numerical solution of variational inequalities for pricing Asian options by higher order Lagrange-Galerkin methods

Applied Numerical Mathematics - Selected papers from the first Chilean workshop on numerical analysis of partial differential equations (WONAPDE 2004)
Stochastic optimal control of ultradiffusion processes with application to dynamic portfolio management

Journal of Computational and Applied Mathematics
Extrapolation discontinuous Galerkin method for ultraparabolic equations

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	7.29

Visualization

Abstract

We consider the approximation of the optimal stopping problem associated with ultradiffusion processes in the context of mathematical finance and the valuation of Asian options. In particular, the value function is characterized as the solution of an ultraparabolic variational inequality. Employing the penalty method and a regularization of the state space, we develop higher-order adaptive approximation schemes which utilize the extrapolation discontinuous Galerkin method in temporal space. Numerical examples are provided in order to demonstrate the approach.