In this paper, we use the algebra to characterise decision‐makers’ representations of risk and uncertainty. We show that risk can be represented by objective probabilities on one part of the algebra, and that uncertainty can be represented by subjective probabilities on the other part....

The probability of nuclear war is a major factor in many important policy questions, but it has gotten little scholarly attention. This paper presents a model for calculating the total probability of nuclear war. The model is based on 14 interrelated scenarios for how nuclear war can break out,...

Starting with J. Muth’s unsupported and unsupportable claims, originally made in 1961, that “rational expectations” were subjective probability distributions that were distributed around a known, true, objective probability distribution, various economists have provided the same type of...

In this paper, we present three remarkable properties of the normal distribution: first that if two independent variables 's sum is normally distributed, then each random variable follows a normal distribution (which is referred to as the Levy Cramer theorem), second a variation of the Levy...

Current estimation methods for the probability of causation (PC) make strong parametric assumptions or are inefficient. We derive a nonparametric influence-function-based estimator for a projection of PC, which allows for simple interpretation and valid inference by making weak structural...

New results on conditional joint probability distributions of first exit times are presented for a continuous-time stochastic process defined as the mixture of Markov jump processes moving at different speeds on the same finite state space, while the mixture occurs at a random time. Such mixture...

Accurate estimation of value-at-risk (VaR) and assessment of associated uncertainty is crucial for both insurers and regulators, particularly in Europe. Existing approaches link data and VaR indirectly by first linking data to the parameter of a probability model, and then expressing VaR as a...

The most commonly employed decision making paradigms are expected utility, prospect theory and regret theory. We examine the simple heuristic of maximizing the probability of being ahead, which in some natural economic situations may be in contradiction to all three of the above fundamental...