1,721,111 research outputs found
Model uncertainty
No full textWe study decision problems in which consequences of the various alternative actions depend on states determined by a generative mechanism representing some natural or social phenomenon. Model uncertainty arises because decision makers may not know this mechanism. Two types of uncertainty result, a state uncertainty within models and a model uncertainty across them. We discuss some two-stage static decision criteria proposed in the literature that address state uncertainty in the first stage and model uncertainty in the second (by considering subjective probabilities over models). We consider two approaches to the Ellsberg-type phenomena characteristic of such decision problems: a Bayesian approach based on the distinction between subjective attitudes toward the two kinds
of uncertainty; and a non-Bayesian approach that permits multiple subjective probabilities. Several applications are used to illustrate concepts as they are introduced
Decision analysis under ambiguity
No full textIn selecting the preferred course of action, decision makers are often uncertain about one or more probabilities of interest. The experimental literature has ascertained that this uncertainty (ambiguity) might affect decision makers’ preferences. Then, the decision maker might wish to incorporate ambiguity aversion in the analysis. We investigate the modeling ambiguity attitudes in the solution of decision analysis problems through functionals well-established in the decision theory literature. We obtain the multiple-event problems for subjective expected utility, smooth ambiguity and maximin decision makers. This allows us to establish the conditions under which these alternative decision makers face equivalent problems. Results for certainty equivalents and risk premia in the presence of both risk and ambiguity aversion are obtained. A recent generalization of the classical Arrow–Pratt quadratic approximation allows us to quantify the portions of a premium due to risk-, and to ambiguity-aversion. The numerical implementation of the objective functions is addressed, showing that all functionals can be estimated at no additional burden through Monte Carlo simulation. The well known Carter Racing case study is addressed quantitatively to demonstrate the findings
On concavity and supermodularity
No full textAbstractConcavity and supermodularity are in general independent properties. A class of functionals defined on a lattice cone of a Riesz space has the Choquet property when it is the case that its members are concave whenever they are supermodular. We show that for some important Riesz spaces both the class of positively homogeneous functionals and the class of translation invariant functionals have the Choquet property. We extend in this way the results of Choquet [G. Choquet, Theory of capacities, Ann. Inst. Fourier (Grenoble) 5 (1953–1954) 131–295] and König [H. König, The (sub/super) additivity assertion of Choquet, Studia Math. 157 (2003) 171–197]
A strong law of large numbers for capacities
No full textWe consider a totally monotone capacity on a Polish space and a sequence of bounded p.i.i.d. random variables. We show that, on a full set, any cluster point of empirical averages lies between the lower and the upper Choquet integrals of the random variables, provided either the random variables or the capacity are continuous
Finitely well-positioned sets
No full textWe introduce and study finitely well-positioned sets, a class of asymptotically “narrow” sets that generalize the well-positioned sets recently investigated by Adly, Ernst and Thera (2001, 2004), as well as the plastering property of Krasnoselskii (1964)
Unique solutions for stochastic recursive utilities
No full textWe study unique and globally attracting solutions of a general nonlinear stochastic equation, widely used in Finance and Macroeconomics and closely related to stochastic Koopmans equations
Weak time-derivatives and no-arbitrage pricing
No full textWe prove a risk-neutral pricing formula for a large class of semimartingale processes through a novel notion of weak time-differentiability that permits to differentiate adapted processes. In particular, the weak time-derivative isolates drifts of semimartingales and is null for martingales. Weak time-differentiability enables us to characterize no-arbitrage prices as solutions of differential equations, where interest rates play a key role. Finally, we reformulate the eigenvalue problem of Hansen and Scheinkman (Econometrica 77:177–234, 2009) by employing weak time-derivatives
Ambiguity aversion and model misspecification: an economic perspective
No full textWe discuss a paper published in Statistical Science by focusing on model misspecification
Mutual absolute continuity of multiple priors
No full textThis note provides a behavioral characterization of mutually absolutely continuous multiple prior
On the cardinal utility equivalence of biseparable preferences
Full text linkWe establish a simple condition, based on the willingness to bet on events, under which two biseparable preferences have cardinally equivalent utilities
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