J.M. Keynes's method in the A Treatise on Probability, inexact measurement and approximation using non additive upper and lower probabilities, is a formal, inductive logic built on G. Boole's original Boolean Algebra and Logic. It has nothing to do with "…a given list of possible behaviors....

We derive a simple integral equation for the default probability over a finite time horizon of a company that makes coupon payments on its debt and infrequently returns to its leverage target by increasing its debt unless it defaults on its debt. Compared to the conventional (constant default...

In this paper we present an evaluation framework for predictions of binary events in probabilistic electricity price forecasting. It employs the MSE-equivalent QPS together with the DM test and allows for further insights about deficiencies of the considered models. Additionally, techniques from...

The spillover index introduced by Diebold and Yilmaz (Economic Journal, 2009, vol. 119, pp. 158-171) is widely used in the analysis of financial market interlinkages. Abrupt increases in the spillover index are thought to be associated with systemic events but formal statistical support for this...

Procedures for constructing the characteristic functions of risk neutral densities, from option prices at a fixed maturity, are developed. The logarithm of these characteristic functions are shown to synthesize the Fourier transform of formal Lévy tails. The formal Lévy tails are actual Lévy...

In the recent Fundamental Review of the Trading Book (FRTB), the Basel Committee on Banking Supervision proposed the shift from the 99% Value-at-Risk (VaR) to the 97.5% Expected Shortfall (ES) for internal models in market risk assessment. Inspired by the above transition, we introduce a new...

How do we combine others' probability forecasts? Prior research has shown that when advisors provide numeric probability forecasts, people typically average them (i.e., they move closer to the average advisor's forecast). However, what if the advisors say that an event is “likely” or...

This study examines the estimation of the exchangeable joint distribution when the highest (lowest) and another order statistics are observable. The estimator would be appropriate for the estimation of the valuation distribution of auctions and "order-biased" sampling, such as school student...

In this paper, we develop some properties to state the relationships between the central moments and stochastic dominance for both the general utility functions and the polynomial utility functions. This leads to draw preferences of both risk averters and risk seekers on their choices of assets...

This paper presents a new asset pricing model incorporating fundamental uncertainties by choice of a probability measure. This approach is novel in that we incorporate uncertainties on Brownian motions describing risks into the existing asset pricing model. Particularly, we show extensions of...