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arXiv · 1601.00919

Exponential integrability properties of Euler discretization schemes for the Cox-Ingersoll-Ross process

Andrei Cozma·Christoph Reisinger
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Abstract

We analyze exponential integrability properties of the Cox-Ingersoll-Ross (CIR) process and its Euler discretizations with various types of truncation and reflection at 0. These properties play a key role in establishing the finiteness of moments and the strong convergence of numerical approximations for a class of stochastic differential equations arising in finance. We prove that both implicit and explicit Euler-Maruyama discretizations for the CIR process preserve the exponential integrability of the exact solution for a wide range of parameters, and find lower bounds on the explosion time.

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Andrei Cozma, Christoph Reisinger. 2015-12-17. Exponential integrability properties of Euler discretization schemes for the Cox-Ingersoll-Ross process. https://arxiv.org/abs/1601.00919

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