We introduce a novel and convenient approach to utility modeling. In doing so, we present a general utility function in a very simple exact form. Furthermore, we develop a method to (accurately) measure preferences without any utility data. We also devise a method to measure the marginal...

We present simple parametric methods that overcome major limitations of the literature on joint/marginal density estimation. In doing so, we do not assume any form of marginal or joint distribution. Furthermore, using our method, a multivariate density can be easily estimated if we know only one...

We present a formal theorem of the square root of the Brownian motion. In doing so, we show that this process can be presented as a typical complex random variable. In addition, we introduce the basic properties of this process

We devise a method to circumvent the complexity that arises from the option multi-dimensionality. That is, we transform the model to make it as simple as the one-dimensional case. Furthermore, the assumption of comonotonicity and other assumptions regarding the structure of the underlying asset...

We provide simple, explicit formulas for pricing both the European and American options. These formulas do not require any numerical/computational methods. Moreover, we provide these formulas understochastic volatility, jumps, both stochastic volatility and stochastic interest rate, and...