Stochastic volatility is the unpredictable nature of asset price volatility over time. It's a flexible alternative to the Black Scholes' constant volatility assumption.

Background Annually, 4% of the global population undergoes non-cardiac surgery, with 30% of those patients having at least ...

Introduction After the WHO prequalified the first vaccine against mpox, we aimed to identify the influence of vaccine ...

Only two men can tell us if Elon Musk and Trump are truly, as of December 2025, “friends.” But the formal definition I used ...

Objectives In patients with chronic obstructive pulmonary disease (COPD), severe exacerbations (ECOPDs) impose significant morbidity and mortality. Current guidelines emphasise using ECOPD history to ...

The total area under the curve must equal 1, representing the fact that the probability of some outcome occurring within the entire range is certain. \[\int_{-\infty}^{\infty}f\left(x\right)dx=1\] ...

A discrete random variable is a type of random variable that can take on a countable set of distinct values. Common examples include the number of children in a family, the outcome of rolling a die, ...

Abstract: Complex random variables arise naturally in many settings and their properties are of general interest. Past work on complex variables has mainly focused on their second-order structure, as ...

Understanding Joint Probability Density Functions | Examples and Key Concepts In this video, we examine joint probability density functions (PDFs), a key concept in probability and statistics that ...

Forecasting for any small business involves guesswork. You know your business and its past performance, but you may not be comfortable predicting the future. Using Excel is a great way to perform what ...