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The concept of conditional expectation is important in applications of probability and statistics in many areas such as reliability engineering, economy, finance, and actuarial sciences due to its property of being the best predictor of a…
Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that typically arise from applying decision rules…
This paper studies a one-sector optimal growth model with i.i.d. productivity shocks that are allowed to be unbounded. The utility function is assumed to be non-negative and unbounded from above. The novel feature in our framework is that…
The sub-linear expectation or called G-expectation is a nonlinear expectation having advantage of modeling non-additive probability problems and the volatility uncertainty in finance. Let $\{X_n;n\ge 1\}$ be a sequence of independent random…
We provide an economic interpretation of the practice consisting in incorporating risk measures as constraints in a classic expected return maximization problem. For what we call the infimum of expectations class of risk measures, we show…
Sets of desirable gambles constitute a quite general type of uncertainty model with an interesting geometrical interpretation. We give a general discussion of such models and their rationality criteria. We study exchangeability assessments…
Assuming that agents' preferences satisfy first-order stochastic dominance, we show how the Expected Utility paradigm can rationalize all optimal investment choices: the optimal investment strategy in any behavioral law-invariant…
Prior work has proposed effective methods to learn event representations that can capture syntactic and semantic information over text corpus, demonstrating their effectiveness for downstream tasks such as script event prediction. On the…
An analyst observes an agent take a sequence of actions. The analyst does not have access to the agent's information and ponders whether the observed actions could be justified through a rational Bayesian model with a known utility…
We consider the problem of decision-making with side information and unbounded loss functions. Inspired by probably approximately correct learning model, we use a slightly different model that incorporates the notion of side information in…
This paper deals with an extended model of computations which uses the parameterized families of entities for data objects and reflects a preliminary outline of this problem. Some topics are selected out, briefly analyzed and arranged to…
Gilboa and Schmeidler's (1989) uncertainty aversion plays a central role in decision theory and economics, yet many inconsistent behaviors have been observed in experiments. Motivated by this, we study an axiom postulating a minimal degree…
In normative models a decision-maker is usually assumed to be Bayesian rational, and so to maximize subjective expected utility, within a complete and correctly specified decision model. Following the discussion in Hammond (2007) of…
We present a new strategic voting model where we use uncertainty representation to model preferences. Specifically, we use probability sets as uncertainty representations, together with lower and upper expected utility gains to take…
We introduce a utility-driven bounded-confidence model of opinion dynamics in which opinions associated with higher utility exert stronger social influence. In the regime where all agents belong to a single opinion cluster, we derive a…
This paper investigates optimal portfolio strategies in a financial market where the drift of the stock returns is driven by an unobserved Gaussian mean reverting process. Information on this process is obtained from observing stock returns…
Despite decades of research in risk management, most of the literature has focused on scalar risk measures (like e.g. Value-at-Risk and Expected Shortfall). While such scalar measures provide compact and tractable summaries, they provide a…
We demonstrate a limitation of discounted expected utility, a standard approach for representing the preference to risk when future cost is discounted. Specifically, we provide an example of the preference of a decision maker that appears…
For the extended skew-normal distribution, which represents an extension of the normal (or Gaussian) distribution, we focus on the properties of the log-likelihood function and derived quantities in the the bivariate case. Specifically, we…
We address the relative expressiveness of defeasible logics in the framework DL. Relative expressiveness is formulated as the ability to simulate the reasoning of one logic within another logic. We show that such simulations must be…