finite difference method

European option pricing under model involving slow growth volatility with jump

In this paper, we suggest a new model for establishing a numerical study related to a European options pricing problem  where assets' prices can be described by a stochastic equation with a discontinuous sample path (Slow Growth Volatility with Jump SGVJ model) which uses a non-standard volatility.  A special attention is given to characteristics of the proposed model represented by its non-standard volatility defined by the parameters $\alpha$ and $\beta$.  The mathematical modeling in the presence of jump shows that one has to resort to a degenerate partial integro-di

Quantifying uncertainty of a mathematical model of drug transport in tumors

This paper presents a numerical simulation in the two-dimensional for a system of PDE governing drug transport in tumors with random coefficients, which is described  as a random field.  The continuous stochastic field is approximated by a finite number of random variables via the Karhunen–Loève expansion and transform the stochastic problem into a determinate one with a parameter in high dimension.  Then we apply a finite difference scheme and the Euler–Maruyama Integrator in time.  The Monte Carlo method is used to compute corresponding simple averages.  We compute the error estimate usin