Optimal Stopping with Dynamic Variational Preferences

We consider optimal stopping problems in uncertain environments for an agent assessing utility by virtue of dynamic variational preferences or, equivalently, assessing risk by dynamic convex risk measures. The solution is achieved by generalizing the approach in terms of multiple priors introducing the concept of variational supermartingales and an accompanying theory. To illustrate results, we consider prominent examples: dynamic entropic risk measures and a dynamic version of generalized average value at risk.optimal Stopping, Uncertainty, Dynamic Variational Preferences, Dynamic Convex Risk Measures, Dynamic Penalty, Time-Consistency, Entropic Risk, Average Value at Risk

Merging of Opinions under Uncertainty

We consider long-run behavior of agents assessing risk in terms of dynamic convex risk measures or, equivalently, utility in terms of dynamic variational preferences in an uncertain setting. By virtue of a robust representation, we show that all uncertainty is revealed in the limit and agents behave as expected utility maximizer under the true underlying distribution regardless of their initial risk anticipation. In particular, risk assessments of distinct agents converge. This result is a generalization of the fundamental Blackwell-Dubins Theorem, cp. [Blackwell & Dubins, 62], to convex risk. We furthermore show the result to hold in a non -time-consistent environment.Dynamic Convex Risk Measures, Multiple Priors, Uncertainty, Robust Representation, Time-Consistency, Blackwell-Dubins.

Merging of Opinions under Uncertainty

We consider long-run behavior of agents assessing risk in terms of dynamic convex risk measures or, equivalently, utility in terms of dynamic variational preferences in an uncertain setting. By virtue of a robust representation, we show that all uncertainty is revealed in the limit and agents behave as expected utility maximizer under the true underlying distribution regardless of their initial risk anticipation. In particular, risk assessments of distinct agents converge. This result is a generalization of the fundamental Blackwell-Dubins Theorem, cp. [Blackwell & Dubins, 62], to convex risk. We furthermore show the result to hold in a non-time-consistent environment.Dynamic Convex Risk Measures, Multiple Priors, Uncertainty, Robust Representation, Time-Consistency, Blackwell-Dubins

On Dynamic Coherent and Convex Risk Measures : Risk Optimal Behavior and Information Gains

We consider tangible economic problems for agents assessing risk by virtue of dynamic coherent and convex risk measures or, equivalently, utility in terms of dynamic multiple priors and dynamic variational preferences in an uncertain environment. Solutions to the Best-Choice problem for a risky number of applicants are well-known. In Chapter 2, we set up a model with an ambiguous number of applicants when the agent assess utility with multiple prior preferences. We achieve a solution by virtue of multiple prior Snell envelopes for a model based on so called assessments. The main result enhances us with conditions for the ambiguous problem to possess finitely many stopping islands. In Chapter 3 we consider general optimal stopping problems for an agent assessing utility by virtue of dynamic variational preferences. Introducing variational supermartingales and an accompanying theory, we obtain optimal solutions for the stopping problem and a minimax result. To illustrate, we consider prominent examples: dynamic entropic risk measures and a dynamic version of generalized average value at risk. In Chapter 4, we tackle the problem how anticipation of risk in an uncertain environment changes when information is gathered in course of time. A constructive approach by virtue of the minimal penalty function for dynamic convex risk measures reveals time-consistency problems. Taking the robust representation of dynamic convex risk measures as given, we show that all uncertainty is revealed in the limit, i.e. agents behave as expected utility maximizers given the true underlying distribution. This result is a generalization of the fundamental Blackwell-Dubins theorem showing coherent as well as convex risk measures to merge in the long run

Gaze Strategy in the Free Flying Zebra Finch (Taeniopygia guttata)

Fast moving animals depend on cues derived from the optic flow on their retina. Optic flow from translational locomotion includes information about the three-dimensional composition of the environment, while optic flow experienced during a rotational self motion does not. Thus, a saccadic gaze strategy that segregates rotations from translational movements during locomotion will facilitate extraction of spatial information from the visual input. We analysed whether birds use such a strategy by highspeed video recording zebra finches from two directions during an obstacle avoidance task. Each frame of the recording was examined to derive position and orientation of the beak in three-dimensional space. The data show that in all flights the head orientation was shifted in a saccadic fashion and was kept straight between saccades. Therefore, birds use a gaze strategy that actively stabilizes their gaze during translation to simplify optic flow based navigation. This is the first evidence of birds actively optimizing optic flow during flight

Azimuthal di-hadron correlations in d+Au and Au+Au collisions at sNN=200\sqrt{s_{NN}}=200 GeV from STAR

Yields, correlation shapes, and mean transverse momenta \pt{} of charged particles associated with intermediate to high-\pt{} trigger particles (2.5 < \pt < 10 \GeVc) in d+Au and Au+Au collisions at \snn=200 GeV are presented. For associated particles at higher \pt \gtrsim 2.5 \GeVc, narrow correlation peaks are seen in d+Au and Au+Au, indicating that the main production mechanism is jet fragmentation. At lower associated particle \pt < 2 \GeVc, a large enhancement of the near- (\dphi \sim 0) and away-side (\dphi \sim \pi) associated yields is found, together with a strong broadening of the away-side azimuthal distributions in Au+Au collisions compared to d+Au measurements, suggesting that other particle production mechanisms play a role. This is further supported by the observed significant softening of the away-side associated particle yield distribution at \dphi \sim \pi in central Au+Au collisions.Comment: 16 pages, 11 figures, updated after journal revie

A Service of zbw Engelage, Daniel Optimal Stopping with Dynamic Variational Preferences Optimal Stopping with Dynamic Variational Preferences Optimal Stopping with Dynamic Variational Preferences

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Merging of opinions under uncertainty

Bier M, Engelage D. Merging of opinions under uncertainty. Working Papers. Institute of Mathematical Economics. Vol 433. Bielefeld: Universität Bielefeld; 2010.We consider long-run behavior of agents assessing risk in terms of dynamic convex risk measures or, equivalently, utility in terms of dynamic variational preferences in an uncertain setting. By virtue of a robust representation, we show that all uncertainty is revealed in the limit and agents behave as expected utility maximizer under the true underlying distribution regardless of their initial risk anticipation. In particular, risk assessments of distinct agents converge. This result is a generalization of the fundamental Blackwell-Dubins Theorem, cp. [Blackwell & Dubins, 62], to convex risk. We furthermore show the result to hold in a non-time-consistent environment

Optimal stopping with dynamic variational preferences

We solve optimal stopping problems in uncertain environments for agents assessing utility by virtue of dynamic variational preferences as in Maccheroni, Marinacci and Rustichini (2006) [16] or, equivalently, assessing risk in terms of dynamic convex risk measures as in Cheridito, Delbaen and Kupper (2006) [4]. The solution is achieved by generalizing the approach in Riedel (2009) [21] introducing the concept of variational supermartingales and variational Snell envelopes with an accompanying theory. To illustrate results, we consider prominent examples: dynamic multiplier preferences and a dynamic version of generalized average value at risk introduced in Cheridito and Tianhui (2009) [5].Optimal stopping Uncertainty aversion Dynamic variational preferences Dynamic convex risk measures Dynamic penalty Time consistency Multiplier preferences Entropic risk Average value at risk