Том 3

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Simulating stochastic diffusion processes and processes with "market" time
(2020) Boluh, Kateryna; Shchestyuk, Nataliia
The paper focuses on modelling, simulation techniques and numerical methods concerned stochastic processes in subject such as financial mathematics and financial engineering. The main result of this work is simulation of a stochastic process with new market active time using Monte Carlo techniques. The processes with market time is a new vision of how stock price behavior can be modeled so that the nature of the process is more real. The iterative scheme for computer modelling of this process was proposed. It includes the modeling of diffusion processes with a given marginal inverse gamma distribution. Graphs of simulation of the Ornstein-Uhlenbeck random walk for different parameters, a simulation of the diffusion process with a gamma-inverse distribution and simulation of the process with market active time are presented.