If the closed-form formula for the probability density function is not available, implementing the maximum likelihood estimation is challenging. We introduce a simple, fast, and accurate way for the estimation of numerous distributions that belong to the class of tempered stable probability...

Carr and Wu (2004), henceforth CW, developed a framework that encompasses almost all of the continuous-time models proposed in the option pricing literature. Their framework hinges on the stopping time property of the time changes. By ana- lyzing the measurability of the time changes with...

Extensions of expected utility theory are sensitive to the tail behavior of the portfolio return distribution and may not be approximated reliably through higher-order moment expansions. We develop a novel approach for model risk assessment based on a projection method and apply it to portfolio...

We develop a novel class of time-changed Lévy models which are tractable and readily applicable, capture the leverage effect, and exhibit pure jump processes with finite or infinite activity. Our models feature four nested processes reflecting market, volatility and jump risks, and observation...

A multi-layer, multi-node ReLU network is a powerful, efficient, and popular tool in statistical prediction tasks. However, in contrast to the great emphasis on its empirical applications, its statistical properties are rarely investigated which is mainly due to its severe nonlinearity and heavy...