We consider some well-known partial differential equations that arise in Financial Mathematics, namely the Black–Scholes–Merton, Longstaff, Vasicek, Cox–Ingersoll–Ross and Heath equations. Our central aim is to discover any underlying connections taking into account Lie remarkability property of heat equation. For a few these there known connection with equation through coordinate transformatio...

the estimate of entropy (sample entropy), has been introduced by vasicek (1976), for the first time. in this paper, we provide an estimate of entropy of order statistics, that is the extention of the entropy estimate. then we present an application of the entropy estimate of order statistics as a test statistic for symmetry of distribution versus skewness. the proposed test has been compared wi...

Different approaches to goodness of fit (GOF) testing are proposed. This survey intends to present the developments on Goodness of Fit based on entropy during the last 50 years, from the very first origins until the most recent advances for different data and models. Goodness of fit tests based on Shannon entropy was started by Vasicek in 1976 and were continued by many authors. In this paper, ...

In this paper we are interested in fractional stochactic differential equations (SDEs) with a soft wall. What do mean by such type of equation? It has been established that SDE reflection can be imagined as having hard Now, introducing repulsion instead reflection, one obtains an contrast to the where process cannot pass wall, wall is repulsive but not impenetrable. As crosses boundary, it expe...