• Bulletin of the Korean Mathematical Society
• /
• v.61 no.4
• /
• pp.917-932
• /
• 2024

In this paper, we deal with the Euler-Maruyama (EM) scheme for stochastic differential equations driven by G-Brownian motion (G-SDEs). Under the linear growth and the local Lipschitz conditions, the strong convergence as well as the rate of convergence of the EM numerical solution to the exact solution for G-SDEs are established.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.4
• /
• pp.1241-1261
• /
• 2018

We derive discrete time model of the geometric fractional Brownian motion. It provides numerical pricing scheme of financial derivatives when the market is driven by geometric fractional Brownian motion. With the convergence analysis, we guarantee the convergence of Monte Carlo simulations. The strong convergence rate of our scheme has order H which is Hurst parameter. To obtain our model we need to convert Wick product term of stochastic differential equation into Wick free discrete equation through Malliavin calculus but ours does not include Malliavin derivative term. Finally, we include several numerical experiments for the option pricing.