Safa' Alsheyab | Searcharxiv

arXiv2025

A new stochastic diffusion process to model and predict electricity production from natural gas sources in the United States

This paper introduces a new stochastic diffusion process to model the electricity production from natural gas sources (as a percentage of total electricity production) in the United States. The method employs trend function analysis to generate fits and forecasts with both conditional and unconditional estimated trend functions. Parameters are estimated using the maximum likelihood (ML) method, based on discrete sampling paths of the variable "electricity production from natural gas sources in the United States" with annual data from 1990 to 2021. The results show that the proposed model effectively fits the data and provides dependable medium-term forecasts for 2022-2023.

stat.AP↗

arXiv2024

Optimal stopping problem under random horizon

This paper considers a pair $(\mathbb{F},τ)$, where $\mathbb{F}$ is a filtration representing the "public" flow of information which is available to all agents overtime, and $τ$ is a random time which might not be an $\mathbb{F}$-stopping time. This setting covers the case of credit risk framework where $τ$ models the default time of a firm or client, and the setting of life insurance where $τ$ is the death time of an agent. It is clear that random times can not be observed before their occurrence. Thus the larger filtration $\mathbb{G}$, which incorporates $\mathbb{F}$ and makes $τ$ observable, results from the progressive enlargement of $\mathbb{F}$ with $τ$. For this informational setting, governed by $\mathbb{G}$, we analyze the optimal stopping problem in three main directions. The first direction consists of characterizing the existence of the solution to this problem in terms of $\mathbb{F}$-observable processes. The second direction lies in deriving the {\it mathematical structures} of the value process of this control problem, while the third direction singles out the associated optimal stopping problem under $\mathbb{F}$. These three aspects allow us to quantify deeply how $τ$ impact the optimal stopping problem, while they are also vital for studying reflected backward stochastic differential equations which arise {\it naturally} from pricing and hedging of vulnerable claims.

math.PR↗