Critical Value-Based Power Options Pricing Problems in Uncertain Financial Markets

Abstract

Compared with investing an ordinary options, investing the power options may possibly yield greater returns. On the one hand, the power option is the best choice for those who want to maximize the leverage of the underlying market movements. On the other hand, power options can also prevent the financial market changes caused by the sharp fluctuations of the underlying assets. In this paper, we investigate the power option pricing problem in which the price of the underlying asset follows the Ornstein–Uhlenbeck type of model involving an uncertain fractional differential equation. Based on critical value criterion, the pricing formulas of European power options are derived. Finally, some numerical experiments are performed to illustrate the results.

Partial Gini Coefficient for Uncertain Random Variables with Application to Portfolio Selection

“…After that, some important contributions were devoted to the application of uncertain random variables, for instance [24][25][26][27][28][29][30]. In the past decades, researchers have proposed various risk measures for uncertain random environments such as variance (Liu [23]), entropy (Sheng et al [31]), partial entropy (Ahmadzade et al [32]; Yang and Zhu [33]), and covariance (Ahmadzade and Gao [34]).…”

Crank–Nicolson method for solving uncertain heat equation

“…If we use the Liu process to model the disturbance in a differential system, then the differential equation evolves into an uncertain differential equation (UDE) (Liu 2008 ). Nowadays, UDE has been researched by many scholars and has been extensively applied in many areas like finance (Chen and Gao 2013 , 2018 ; Yang and Zhu 2021 ), dynamic games (Yang and Gao 2016 ; Zhang et al. 2021 ) and COVID-19 spread (Lio 2021 ).…”