This paper presents a novel approach to portfolio optimization based on perceived mean reversion in certain driftless markets, such as the foreign exchange spot market. This approach relies upon the likelihood ratio between the perceived and realized price distribution densities of the asset...

We present a new method to sample random variables through the use of orthogonal polynomial expansions of the associated quantile function that utilize the inverse transform technique. In particular, we obtain an explicit representation of the quantile function through an orthogonal expansion...

We show that during the weeks following the initiation of the COVID-19 pandemic, the United States equity market was inefficient. This is demonstrated by showing that utility maximizing agents over the time period ranging from mid-February to late March 2020 can generate statistically...

We frame linear factor models for asset pricing in a machine learning context and consider a numerical comparison of their performance against ordinary least squares linear regression over a dataset of anomaly portfolios. Specific regression models involved in the comparison include regularized...

In this paper, we derive a closed-form explicit model-free formula for the (Black-Scholes) implied volatility. The method is based on the novel use of the Dirac Delta function, corresponding delta families, and the change of variable technique. The formula is expressed through either a limit or...

Traditional plain vanilla options can be regarded as options on a simple return. These options have convex payoffs and as a consequence of Jensen's inequality, their prices are increasing as a function of maturity in the absence of interest rate. This makes long dated call options as excessively...

Information Geometry provides a correspondence between differential geometry and statistics through the Fisher Information matrix. In particular, given two models from the same parametric family of distributions, one can define the distance between these models as the length of the shortest...

We propose an explicit closed-form approximation formula for the price of discretely monitored single or double barrier options whose underlying asset evolves according to a generic one-dimensional Markov process. This set of stochastic processes includes, but is not limited to, diffusion and...