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In the present article we use the quantum formalism to describe the effects of risk and ambiguity in decision theory. The main idea is that the probabilities in the classic theory of expected utility are estimated probabilities, and thus do…
In the paper there is studied an optimal saving model in which the interest-rate risk for saving is a fuzzy number. The total utility of consumption is defined by using a concept of possibilistic expected utility. A notion of possibilistic…
We use a series of pre-registered, incentive-compatible online experiments to investigate how people evaluate and choose among different waiting time distributions. Our main findings are threefold. First, consistent with prior literature,…
Pretrial risk assessment tools are used on over one million U.S. defendants each year, yet their use for predicting rare violent re-offense faces a basic statistical barrier. We derive a universal precision bound -- the Likelihood Ratio…
Shafer's theory of belief and the Bayesian theory of probability are two alternative and mutually inconsistent approaches toward modelling uncertainty in artificial intelligence. To help reduce the conflict between these two approaches,…
We ask if participants in a choice experiment with repeated presentation of the same menus and no feedback provision: (i) exhibit overall behaviour that is consistent with ordinal and expected utility theory under *weak* preferences; (ii)…
We study the connection between risk aversion, number of consumers and uniqueness of equilibrium. We consider an economy with two goods and $c$ impatience types, where each type has additive separable preferences with HARA Bernoulli utility…
Expected Shortfall (ES) has been widely accepted as a risk measure that is conceptually superior to Value-at-Risk (VaR). At the same time, however, it has been criticised for issues relating to backtesting. In particular, ES has been found…
This survey reviews recent developments in revealed preference theory. It discusses the testable implications of theories of choice that are germane to specific economic environments. The focus is on expected utility in risky environments;…
Under expected utility the local index of absolute risk aversion has played a central role in many applications. Besides, its link with the "global" concepts of the risk and probability premia has reinforced its attractiveness. This paper…
Expected Shortfall (ES, also known as CVaR) is the most important coherent risk measure in finance, insurance, risk management, and engineering. Recently, Wang and Zitikis (2021) put forward four economic axioms for portfolio risk…
The equity risk premium puzzle is that the return on equities has far exceeded the average return on short-term risk-free debt and cannot be explained by conventional representative-agent consumption based equilibrium models. We review a…
A utility function has been proposed that values more those lives that are saved by not imposing a harmful treatment and values less those lives that could be saved by treating people who would otherwise die. I do not dispute the ethical…
The prospects of Kahneman and Tversky, Mega Million and Powerball lotteries, St. Petersburg paradox, premature profits and growing losses criticized by Livermore are reviewed under an angle of view comparing mathematical expectations with…
We analyze the convergence of expected utility under the approximation of the Black-Scholes model by binomial models. In a recent paper by D. Kreps and W. Schachermayer a surprising and somewhat counter-intuitive example was given: such a…
Although expected utility theory has proven a fruitful and elegant theory in the finite realm, attempts to generalize it to infinite values have resulted in many paradoxes. In this paper, we argue that the use of John Conway's surreal…
Classical reinforcement learning (RL) techniques are generally concerned with the design of decision-making policies driven by the maximisation of the expected outcome. Nevertheless, this approach does not take into consideration the…
The random utility model (RUM, McFadden and Richter, 1990) has been the standard tool to describe the behavior of a population of decision makers. RUM assumes that decision makers behave as if they maximize a rational preference over a…
People often deviate from expected utility theory when making risky and intertemporal choices. While the effects of probabilistic risk and time delay have been extensively studied in isolation, their interplay and underlying theoretical…
It is well known that Expected Shortfall (also called Average Value-at-Risk) is a convex risk measure, i. e. Expected Shortfall of a convex linear combination of arbitrary risk positions is not greater than a convex linear combination with…