In this paper, we develop and analyze a high order compact finite difference method (CFDM)
for solving a general class of two-point nonlinear singular boundary value problems with …

In this paper we develop a numerical method for a nonlinear parabolic partial differential
equation arising from pricing European options under transaction costs. The method is …

We derive a new high-order compact finite difference scheme for option pricing in stochastic
volatility models. The scheme is fourth order accurate in space and second order accurate in …

In this paper we analyze a nonlinear Black–Scholes model for option pricing under variable
transaction costs. The diffusion coefficient of the nonlinear parabolic equation for the price V …

Proper pricing of options in the financial derivative market is crucial. For many options, it is
often impossible to obtain analytical solutions to the Black–Scholes (BS) equation. Hence an …

In this paper, a new second-order exponential time differencing (ETD) method based on the
Cox and Matthews approach is developed and applied for pricing American options with …

American option prices with M-regime switching satisfy a system of M free boundary value
problems, which is challenging to solve, particularly for large M. In this article, we present an …

We derive high-order compact finite difference schemes for option pricing in stochastic
volatility models on non-uniform grids. The schemes are fourth-order accurate in space and …

There are numerous financial problems that can be posed as optimal control problems,
leading to Hamilton–Jacobi–Bellman or Hamilton–Jacobi–Bellman–Issacs equations. We …

Due to transaction costs, illiquid markets, large investors or risks from an unprotected
portfolio the assumptions in the classical Black–Scholes model become unrealistic and the …