Using an Euler discretization to simulate a mean-reverting CEV process gives rise to the
problem that while the process itself is guaranteed to be nonnegative, the discretization is …

Numerical integration methods for stochastic volatility models in financial markets are
discussed. We concentrate on two classes of stochastic volatility models where the volatility …

Convergence, consistency, stability and pathwise positivity of balanced Milstein methods for
numerical integration of ordinary stochastic differential equations (SDEs) are discussed. This …

In many applications, differential equation models require geometric integration, ie, the
application of structure-preserving integration schemes. In computational finance, for …

In this paper we discuss split-step backward balanced Milstein methods for solving Itô
stochastic differential equations (SDEs). Four families of methods, a family of drifting split …

In this paper, we present the composite Milstein methods for the strong solution of Ito
stochastic differential equations. These methods are a combination of semi-implicit and …

Using an Euler discretisation to simulate a mean-reverting CEV process gives rise to the
problem that while the process itself is guaranteed to be nonnegative, the discretisation is …

The behaviour of ion channels within cardiac and neuronal cells is intrinsically stochastic in
nature. When the number of channels is small this stochastic noise is large and can have an …

The famous Black-Scholes model was the starting point of a new financial industry and has
been a very important pillar of all options trading since. One of its core assumptions is that …

Biochemical pathways involving chemical kinetics in medium concentrations (ie, at
mesoscale) of the reacting molecules can be approximated as chemical Langevin equations …