The Euler-Maruyama approximation for the absorption time of the CEV diffusion

Pavel Chigansky; Fima C. Klebaner

doi:10.3934/dcdsb.2012.17.1455

Article Contents

2012, Volume 17, Issue 5: 1455-1471. Doi: 10.3934/dcdsb.2012.17.1455

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The Euler-Maruyama approximation for the absorption time of the CEV diffusion

Pavel Chigansky^1, and
Fima C. Klebaner^2,

1.
Department of Statistics, The Hebrew University, Mount Scopus, Jerusalem 91905
2.
School of Mathematical Sciences, Monash University Vic 3800

Received: July 31, 2011

Revised: December 31, 2011

Published: June 2012

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Abstract

The standard convergence analysis of the simulation schemes for the hitting times of diffusions typically requires non-degeneracy of their coefficients on the boundary, which excludes the possibility of absorption. In this paper we consider the CEV diffusion from the mathematical finance and show how a weakly consistent approximation for the absorption time can be constructed, using the Euler-Maruyama scheme.

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Mathematics Subject Classification: Primary: 60H10, 60H35; Secondary: 60F17, 91G60.

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