The theorem of existence of the ruptures in the probability scale has been proved for a discrete case. The theorem can be used, e.g., in economics and forecasting. It can assist to solve paradoxes such as Allais paradox and the “four-fold-pattern” paradox and to create the correcting formula...

The theorems of existence of the ruptures have been proved. The ruptures can exist near the borders of finite intervals and of the probability scale. The theorems can be used, e.g., in economics and forecasting.

The understanding of joint asset return distributions is an important ingredient for managing risks of portfolios. While this is a well-discussed issue in fixed income and equity markets, it is a challenge for energy commodities. In this paper we are concerned with describing the joint return...

We propose an asset pricing model with generalized disappointment aversion preferences and long-run volatility risk. With Markov switching fundamentals, we derive closed-form solutions for all returns moments and predictability regressions. The model produces first and second moments of...

I derive and test multi-horizon implications of a consumption-based equilibrium model featuring fluctuating expected growth and volatility. My setup allows consumption dynamics to be estimated jointly with covariance risk prices in a single-stage GMM, and then inferences from asset pricing...

Using the Bayesian posterior distribution of the market parameters we define self-adjusting uncertainty regions for the robust mean-variance problem. Under a normal-inverse-Wishart conjugate assumption for the market, the ensuing robust Bayesian mean-variance optimal portfolios are shrunk by the...

We review the main processes used to model financial variables. We emphasize the parallel between discrete-time processes, mainly used by econometricians for risk- and portfolio-management, and their continuous-time counterparts, mainly used by mathematicians to price derivatives. We highlight...

The Black-Litterman and related approaches modify the return distribution of a normally distributed market according to views or stress-test scenarios. We discuss how to broaden the range of applications of these approaches significantly by letting them act on the risk factors underlying the...

We describe a simple recursive routine to estimate by maximum likelihood the correlation matrix and the degrees of freedom of the t-copula, when structure needs to be imposed on the eigenvalues for dimensionality issues

We walk the reader through the Black-Litterman approach, providing all the proofs. We show how minor modifications of the original model greatly improve its range of applications. We discuss full generalizations of this and related models. MATLAB code is available through MATLAB Central