Exponential Stability of Fractional Large-Scale Neutral Stochastic Delay Systems with Fractional Brownian Motion

T. Sathiyaraj (), T. Ambika and Ong Seng Huat
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T. Sathiyaraj: Institute of Actuarial Science and Data Analytics, UCSI University, Kuala Lumpur 56000, Malaysia
T. Ambika: Department of Computer Science, Rev. Jacob Memorial Christian College, Dindigul 624612, India
Ong Seng Huat: Institute of Actuarial Science and Data Analytics, UCSI University, Kuala Lumpur 56000, Malaysia

JRFM, 2023, vol. 16, issue 5, 1-15

Abstract: Mathematics plays an important role in many fields of finance. In particular, it presents theories and tools widely used in all areas of finance. Moreover, fractional Brownian motion (fBm) and related stochastic systems have been used to model stock prices and other phenomena in finance due to the long memory property of such systems. This manuscript provides the exponential stability of fractional-order Large-Scale neutral stochastic delay systems with fBm. Based on fractional calculus (FC), R n stochastic space and Banach fixed point theory, sufficiently useful conditions are derived for the existence of solution and exponential stability results. In this study, we tackle the nonlinear terms of the considered systems by applying local assumptions. Finally, to verify the theoretical results, a numerical simulation is provided.

Keywords: dynamic risk in asset pricing; exponential stability; finance modeling and derivatives; fractional calculus; fractional Brownian motion; large dimensional problems; simulation and computation in long short-term memory; time delay (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2023
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