Time series analysis of daily stock data and building predictive models are complicated. This
paper presents a comparative study for stock price prediction using three different methods …

In this paper we present a numerical method for a time-fractional Black–Scholes equation,
which is used for modeling the fractional structure of the financial market. The method is …

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 …

A generalized Black–Scholes equation is considered on the semi-axis. It is transformed on
the interval (0, 1) in order to make the computational domain finite. The new parabolic …

The purpose of this review paper is to present our recent results on nonlinear and nonlocal
mathematical models arising from modern financial mathematics. It is based on our four …

In this paper robust algorithms for numerical identification of time dependent volatility by
integral observations of one-and two-asset Black–Scholes models are developed. An …

This paper presents a robust and fast numerical algorithm to reconstruct the implied volatility
as a piecewise linear function of time. This is done from a set of market observations in the …

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 …

We propose and analyse a method based on the Riccati transformation for solving the
evolutionary Hamilton–Jacobi–Bellman equation arising from the dynamic stochastic …

In this work we consider Cauchy problem for the so called Gamma equation, which can be
derived by transforming the fully nonlinear Black–Scholes equation for option price into a …