TStability of the EulerMaruyama Algorithm for the Generalized BlackScholes Model with Fractional Brownian Motion
Volume 14, Number 4, April 2018, pp. 815820 DOI: 10.23940/ijpe.18.04.p23.815820
^{Hui Yu}
College of Science, Heilongjiang Bayi Agricultural University, Daqing, 163319, China
(Submitted on December 21, 2017; Revised on January 29, 2018; Accepted on March 5, 2018)
Abstract:
On account of the fact that a fractional Brownian motion (fBm) with the Hurst parameter H ∈(0,1/2)∪(1/2,1) cannot follow the laws of the semimartingale and the Markov process, little work is presented about the Tstability for stochastic differential equations (SDEs) with fBm. Here, three results are obtained for the generalized BlackScholes model (SDE) with H∈(1/3,1/2). Firstly, the sufficient conditions of the stochastical and asymptotical stability in the large for such equation are presented by the aid of the Lyapunov exponent. Secondly, the EulerMaruyama (EM) numerical algorithm with a given stepsize for such model is constructed. Lastly, by taking advantage of the stable average function, the sufficient conditions of the Tstability that originated from the EM algorithm are presented. All the results show that on the basis of the stability of such equation, the Tstable region produced by the EM algorithm can be found. Moreover, one numerical example is afforded to the main conclusions.
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