Right-tailed distributions are very important in many applications. There studies estimating the tail index. In this paper, we will estimate parameter  using three (the Direct, Bootstrap and Double Bootstrap) methods. Our aim is to illustrate best way   -stable with simulation real data for daily Iraqi financial market dataset.

The first passage time problem has attracted considerable research interest in the field of stochastic processes. It concerns the estimation of the probability density of the time for a random process to cross a specified boundary level. Even though there are many theoretical advances in solving this problem, for many classes of random processes no analytical solution exists. The jumpdiffusion ...

We seek to determine the optimal amount of the insurer’s investment in all types of assets for a small and closed economy. The goal is to detect the implications and contributions the risk seeker and risk aversion insurer commonly make and the effectiveness in the investment decision. Also, finding the optimum portfolio for each is the main goal of the present study. To this end, we adopted the...

dynamics of the mixed-state geometric phase of dissipative qubits. Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. We investigate the geometric phase of a two-leve...

Abstract A slow–fast system with jump-diffusion processes is considered. The large deviations are established via the weak convergence approach, which based on variational representations for functional of Poisson random measure and Brownian motion. We present an example to verify that level asset price satisfies small volatility.