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Sharpe et al. proposed the idea of having an expected utility maximizer choose a probability distribution for future wealth as an input to her investment problem instead of a utility function. They developed a computer program, called The…
We revisit the problem of pricing options with historical volatility estimators. We do this in the context of a generalized GARCH model with multiple time scales and asymmetry. It is argued that the reason for the observed volatility risk…
In 2017-2020 Jordanova and co-authors investigate probabilities for p-outside values and determine them in many particular cases. They show that these probabilities are closely related to the concept for heavy tails. Tukey's boxplots are…
Recent analysis of social communications among humans has revealed that the interval between interactions for a pair of individuals and for an individual often follows a long-tail distribution. We investigate the effect of such a…
The quantitative analysis of financial time series often reveals two distinct features that standard Gaussian frameworks fail to capture: heavy-tailed marginal distributions and the phenomenon of extreme co-movements.While extreme value…
This mathematical recreation extends the analysis of a recent paper, asking when a traveller at a bus stop and not knowing the time of the next bus is best advised to wait or to start walking toward the destination. A detailed analysis and…
Most people are risk-averse (risk-seeking) when they expect to gain (lose). Based on a generalization of ``expected utility theory'' which takes this into account, we introduce an automaton mimicking the dynamics of economic operations.…
Distributed storage systems often employ erasure codes to achieve high data reliability while attaining space efficiency. Such storage systems are known to be susceptible to long tails in response time. It has been shown that in modern…
In the study of large scale stochastic networks with resource management, differential equations and mean-field limits are two key techniques. Recent research shows that the expected fraction vector (that is, the tailed probability vector)…
We consider an investor, whose portfolio consists of a single risky asset and a risk free asset, who wants to maximize his expected utility of the portfolio subject to managing the Value at Risk (VaR) assuming a heavy tailed distribution of…
Two models of a queue are proposed: a human queue and two lines of vehicles before a narrowing. In both models, a queuer tries to evaluate his waiting time, taking into account the delay caused by intruders who jump to the queue front. As…
Algorithmic decision-making in high-stakes settings can have profound impacts on individuals and populations. While much prior work studies fairness in static settings, recent results show that enforcing static fairness constraints may…
Human dynamics is known to be inhomogeneous and bursty but the detailed understanding of the role of human factors in bursty dynamics is still lacking. In order to investigate their role we devise an agent-based model, where an agent in an…
Heavy-tailed probability distributions are extremely useful and play a crucial role in modeling different types of financial data sets. This study presents a two-pronged methodology. First, a mixture probability distribution is created by…
The increasing penetration of embedded renewables makes forecasting net-load, consumption less embedded generation, a significant and growing challenge. Here a framework for producing probabilistic forecasts of net-load is proposed with…
When a particle moves through a spatially-random force field, its momentum may change at a rate which grows with its speed. Suppose moreover that a thermal bath provides friction which gets weaker for large speeds, enabling high-energy…
Decision-making problems often feature uncertainty stemming from heterogeneous and context-dependent human preferences. To address this, we propose a sequential learning-and-optimization pipeline to learn preference distributions and…
We study a temporal voting model where voters have dynamic preferences over a set of public chores -- projects that benefit society, but impose individual costs on those affected by their implementation. We investigate the computational…
Estimation of tail quantities, such as expected shortfall or Value at Risk, is a difficult problem. We show how the theory of nonlinear expectations, in particular the Data-robust expectation introduced in [5], can assist in the…
Web sites where users create and rate content as well as form networks with other users display long-tailed distributions in many aspects of behavior. Using behavior on one such community site, Essembly, we propose and evaluate plausible…