arXiv subjects

Malkhaz Shashiashvili

Publications and source records attributed to Malkhaz Shashiashvili.

2 recordsLinked to original sources

arXiv2021

The Stochastic Balance Equation for the American Option Value Function and its Gradient

In the paper we consider the problem of valuation and hedging of American options written on dividend-paying assets whose price dynamics follow the multidimensional diffusion model. We derive a stochastic balance equation for the American option value function and its gradient. We prove that the latter pair is the unique solution of the stochastic balance equation as a result of the uniqueness in the related adapted future-supremum problem.

q-fin.PR↗

arXiv2018

Estimation of the weighted integrated square error of the Grenander estimator by the Kolmogorov-Smirnov statistic

We consider in this paper the Grenander estimator of unbounded, in general, nonincreasing densities on the interval [0; 1] without any smoothness assumptions. For fixed number n of i.i.d. random vari- ables X1;X2; : : : ;Xn with values in [0; 1] and the nonincreasing den- sity function f(x), 0 < x < 1, we prove an inequality bounding the weighted integrated square error of the Grenander estimator with probability one by the classical Kolmogorov-Smirnov statistic. Fur- ther, we consider some interesting implications of the latter inequality

math.ST↗