Brownian dynamics serve as mathematical models for the diffusive motion of microscopic
particles of various shapes in gaseous, liquid, or solid environments. The renewed interest …

In this paper, we investigate the pricing problem of barrier options under the Heston model.
We innovatively develop a two-step solution process and present an analytical …

This work generalizes a multilevel forward Euler Monte Carlo method introduced in Michael
B. Giles.(Michael Giles. Oper. Res. 56 (3): 607–617, 2008.) for the approximation of …

We present an adaptive multilevel Monte Carlo (MLMC) method for weak approximations of
solutions to Itô stochastic differential equations (SDE). The work [Oper. Res. 56 (2008), 607 …

We derive a posteriori error estimates for the (stopped) weak Euler method to discretize SDE
systems which emerge from the probabilistic reformulation of elliptic and parabolic (initial) …

Construction of splitting-step methods and properties of related nonnegativity and boundary
preserving semianalytic numerical algorithms for solving stochastic differential equations …

The aim of this paper is to derive an approximation formula for a single barrier option under
local volatility models, stochastic volatility models, and their hybrids, which are widely used …

This work develops adaptive time stepping algorithms for the approximation of a functional
of a diffusion with jumps based on a jump augmented Monte Carlo Euler–Maruyama …

Convergence rates of adaptive algorithms for weak approximations of Itoˆ stochastic
differential equations are proved for the Monte Carlo Euler method. Two algorithms based …

A new Monte Carlo method is presented to compute the prices of barrier options on stocks.
The key idea of the new method is to use an exit probability and uniformly distributed …