In this paper, we study a firm's dynamic pricing problem in the presence of unknown and time-varying heterogeneity in customers' preferences for quality. The firm offers a standard product as well as a premium product to deal with this heterogeneity. First, we consider a benchmark case in which...

J M Keynes's two logical relations of rational degree of probability, α, 0≤α≤1 and Evidential Weight of the Argument, w, 0≤w≤1, where w measures the degree of completeness of the evidence, can't be represented or associated with ordinal probability, although Keynes's theory of...

The Markov inequality is a classical nice result in statistics that serves to demonstrate other important results as the Chebyshev inequality and the weak law of large numbers, and that has useful applications in the real world, when the random variable is unspecified, to know an upper bound for...

Although survey-based point predictions have been found to outperform successful forecasting models, corresponding variance forecasts are frequently diagnosed as heavily distorted. Forecasters who report inconspicuously low ex-ante variances often produce squared forecast errors that are much...

Although survey-based point predictions have been found to outperform successful forecasting models, corresponding variance forecasts are frequently diagnosed as heavily distorted. Forecasters who report inconspicuously low ex-ante variances often produce squared forecast errors that are much...

We present a portable model of distorted learning which embodies Tversky and Kahneman's (1971) “belief in the law of small numbers.” When adjusting beliefs in response to new information the decision maker overweights the sample, updating as if the sample size were inflated. The degree of...

A major error in analyzing how Keynes operationalized his logical theory of probability in 1921 is to assume that Keynes's theoretical structure is presented by him at the end of Chapter III of the A Treatise on Probability on pp. 38-40, which contains a diagram on page 39 that Keynes himself...

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...

Keynes's logical theory of probability was NOT the first explicit and detailed approach to logical probability. George Boole was the first academic to provide an explicit, systematic and detailed logical probability approach in history. Keynes's own logical theory was built on both the work of...