EXPONENTIAL INTEGRABILITY PROPERTIES OF EULER DISCRETIZATION SCHEMES FOR THE COX-INGERSOLL-ROSS PROCESS

被引：8
|
作者：
Cozma, Andrei [1 ]
Reisinger, Christoph [1 ]
机构：
[1] Univ Oxford, Math Inst, Oxford OX2 6GG, England
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2016年 / 21卷 / 10期
基金：
英国工程与自然科学研究理事会;
关键词：
Cox-Ingersoll-Ross process; exponential integrability; explicit Euler scheme; implicit Euler scheme; stochastic volatility model; STOCHASTIC VOLATILITY; CONVERGENCE; CIR; OPTIONS; MODEL;
D O I：
10.3934/dcdsb.2016101
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study exponential integrability properties of the Cox-Ingersoll Ross (CIR) process and its Euler-Maruyama 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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页码：3359 / 3377
页数：19
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