This paper proposes a new approximation method for pricing barrier options with discrete monitoring under stochastic volatility environment. In particular, the integration-by-parts formula and the duality formula in Malliavin calculus are effectively applied in pricing barrier options with...

Motivated by weak convergence results in the paper of Takahashi & Yoshida (2005), we show strong convergence for an accelerated Euler–Maruyama scheme applied to perturbed stochastic differential equations. The Milstein scheme with the same acceleration is also discussed as an extended result....

Various international bodies and non-governmental organizations (NGOs) have proposed guidelines for safeguarding biodiversity. Nevertheless, quantitative criteria for safeguarding biodiversity should first be established to measure the attainment of biodiversity conservation if biodiversity is...

This paper shows an explicit small time expansion formula of expectation of the solution to Young SDEs driven by fractional Brownian motion H1/2. The expansion coefficients are obtained by using Malliavin calculus for fractional Brownian motion. Furthermore, we show an analytically tractable...