Three innovative concepts are combined here to create a new and unique framework for optimizing a portfolio of investments or bets. These inventions are:1) The Probability Frontier, a generalization of the Markowitz Efficient Frontier;2) The Positive Probability Estimate, which estimates the...

We evaluate the empirical validity of popular asset-pricing models in explicit consideration of statistical power, by employing the adaptive significance level and equal-probability test. Past studies often use samples from a large cross-section of portfolios over a long time period, conducting...

This paper characterizes U.S. consumption dynamics from the perspective of a Bayesian agent who does not know the underlying model structure but learns over time from macroeconomic data. Realistic, high-dimensional macroeconomic learning problems, which entail parameter, model, and state...

The quotient of random variables with normal distributions is examined and proven to have have power law decay, with density f(x)~f_0 x^(-2), with the coefficient depending on the means and variances of the numerator and denominator, and their correlation. We also obtain the conditional...

We present an alternative derivation of the transition density in the Cox-Ingersoll-Ross (CIR) model. Applying methods developed in elementary quantum mechanics we show that the transition density can be determined from the eigenvalue problem of a second order differential operator with...