Survival with ambiguity

We analyze a market populated by expected utility maximizers and smooth ambiguity-averse consumers. We study conditions under which ambiguity-averse consumers survive and a¤ect prices in the limit. If ambiguity vanishes with time or if the economy exhibits no aggregate risk, ambiguity-averse consumers survive, but have no long-run impact on prices. In both scenarios, ambiguity-averse consumers are fully insured against ambiguity in equilibrium and, thus, behave as expected utility maximizers with correct beliefs. If ambiguity-averse consumers are not fully insured against ambiguity, they behave as expected utility maximiz- ers with e¤ectively wrong beliefs and an e¤ective discount factor which might be higher or lower than their actual discount factor. Using this in- sight, we demonstrate that consumers with constant absolute ambiguity aversion vanish in expectations, whenever the economy faces aggregate risk. In contrast, consumers with constant relative (and thus, decreas- ing absolute) ambiguity aversion survive in expectation and with positive probability and have a non-trivial impact on prices in the limit

Making Space for Stories: Ambiguity in the Design of Personal Communication Systems

Pervasive personal communication technologies offer the potential for important social benefits for individual users, but also the potential for significant social difficulties and costs. In research on face-to-face social interaction, ambiguity is often identified as an important resource for resolving social difficulties. In this paper, we discuss two design cases of personal communication systems, one based on fieldwork of a commercial system and another based on an unrealized design concept. The cases illustrate how user behavior concerning a particular social difficulty, unexplained unresponsiveness, can be influenced by technological issues that result in interactional ambiguity. The cases also highlight the need to balance the utility of ambiguity against the utility of usability and communicative clarity.Comment: 10 page

Optimal Investments for Risk- and Ambiguity-Averse Preferences: A Duality Approach

Ambiguity, also called Knightian or model uncertainty, is a key feature in financial modeling. A recent paper by Maccheroni et al. (2004) characterizes investor preferences under aversion against both risk and ambiguity. Their result shows that these preferences can be numerically represented in terms of convex risk measures. In this paper we study the corresponding problem of optimal investment over a given time horizon, using a duality approach and building upon the results by Kramkov and Schachermayer (1999, 2001).Model uncertainty, ambiguity, convex risk measures, optimal investments, duality theory

The pronouncements of paranoid politicians

This paper models the strategic encounter of two office-motivated candidates who may or may not announce policy. In the case of no announcement, the voters rank the candidates according to prior beliefs. In the case of announcement, the candidates cannot avoid a degree of noise in the voters' interpretation of their announcements. We show that this simple deviation from the standard Downsian setting suffices to overcome previous impossibility results which suggest that not announcing policy can never occur in equilibrium. Also, we extend the model to study the equilibrium when candidates are ambiguity averse. An ambiguity averse candidate is interpreted as being concerned about an ongoing negative campaign against him. This negative campaign would consist in inducing the voters to adopt some interpretation of the candidate's announcement unfavorable to his electoral performance. We show that under ambiguity aversion the candidates opt not to announce position under less stringent conditions than expected utility. Finally, we use data on U.S. Senate elections to test an empirical implication of the model. We find that the relevant coefficient has the sign predicted by the theory and is statistically significant.Voting; Salience; Electoral Ambiguity; Ambiguity Aversion; Media Politics

Analysis of approximate nearest neighbor searching with clustered point sets

We present an empirical analysis of data structures for approximate nearest neighbor searching. We compare the well-known optimized kd-tree splitting method against two alternative splitting methods. The first, called the sliding-midpoint method, which attempts to balance the goals of producing subdivision cells of bounded aspect ratio, while not producing any empty cells. The second, called the minimum-ambiguity method is a query-based approach. In addition to the data points, it is also given a training set of query points for preprocessing. It employs a simple greedy algorithm to select the splitting plane that minimizes the average amount of ambiguity in the choice of the nearest neighbor for the training points. We provide an empirical analysis comparing these two methods against the optimized kd-tree construction for a number of synthetically generated data and query sets. We demonstrate that for clustered data and query sets, these algorithms can provide significant improvements over the standard kd-tree construction for approximate nearest neighbor searching.Comment: 20 pages, 8 figures. Presented at ALENEX '99, Baltimore, MD, Jan 15-16, 199

Survival with ambiguity

We analyze a market populated by expected utility maximizers and smooth ambiguity-averse consumers. We study conditions under which ambiguity-averse consumers survive and affect prices in the limit. If ambiguity vanishes with time or if the economy exhibits no aggregate risk, ambiguity-averse consumers survive, but have no long-run impact on prices. In both scenarios ambiguity-averse consumers are fully insured against ambiguity in equilibrium and thus behave as expected utility maximizers with correct beliefs. If ambiguity-averse consumers are not fully insured against ambiguity, their behavior mimics expected utility maximizers with wrong beliefs and a stochastic discount factor which might be consistently higher or lower than their actual discount factor. We use this insight to analyze a Markov economy with large persistent ambiguity. Consumers with decreasing absolute ambiguity aversion whose prudence with respect to ambiguity exceeds twice their absolute ambiguity aversion a.s. survive in the presence of expected utility maximizers with correct beliefs. If the economy further exhibits aggregate risk, they drive the expected utility maximizers out of the market and determine prices in the limit. In contrast, consumers with increasing or constant absolute ambiguity aversion only survive in the absence of aggregate risk and have no impact on limit prices

Does Political Ambiguity Pay? Corporate Campaign Contributions and the Rewards to Legislator Reputation

Do politicians tend to follow a strategy of ambiguity in their policy positions or a strategy of reputational development to reduce uncertainty about where they stand? Ambiguity could allow a legislator to avoid alienating constituents and to play rival interests off against each other to maximize campaign contributions. Alternatively, reputational clarity could help to reduce uncertainty about a candidate and lead to high campaign contributions from favored interests. We outline a theory that considers conditions under which a politician would and would not prefer reputational development and policy-stance clarity in the context of repeat dealing with special interests. Our proxy for reputational development is the percent of repeat givers to a legislator. Using data on corporate political action committee contributions (PACs) to members of the U.S. House during the seven electoral cycles from 1983/84 to 1995/96, we find that legislators do not appear to follow a strategy of ambiguity and that high reputational development is rewarded with high PAC contributions.

Uncertainty Averse Preferences

We study uncertainty averse preferences, that is, complete and transitive preferences that are convex and monotone. We establish a representation result, which is at same time general and rich in structure. Many objective functions commonly used in applications are special cases of this representation.ambiguity aversion, games against nature, model uncertainty, smooth ambiguity preferences, variational preferences

A unified approach to χ2\chi^2 discriminators for searches of gravitational waves from compact binary coalescences

We describe a general mathematical framework for $\chi^2$ discriminators in the context of the compact binary coalescence search. We show that with any $\chi^2$ is associated a vector bundle over the signal manifold, that is, the manifold traced out by the signal waveforms in the function space of data segments. The $\chi^2$ is then defined as the square of the $L_2$ norm of the data vector projected onto a finite dimensional subspace (the fibre) of the Hilbert space of data trains and orthogonal to the signal waveform - any such fibre leads to a $\chi^2$ discriminator and the full vector bundle comprising the subspaces and the base manifold constitute the $\chi^2$ discriminator. We show that the $\chi^2$ discriminators used so far in the CBC searches correspond to different fiber structures constituting different vector bundles on the same base manifold, namely, the parameter space. The general formulation indicates procedures to formulate new $\chi^2$s which could be more effective in discriminating against commonly occurring glitches in the data. It also shows that no $\chi^2$ with a reasonable degree of freedom is foolproof. It could also shed light on understanding why the traditional $\chi^2$ works so well. As an example, we propose a family of ambiguity $\chi^2$ discriminators that is an alternative to the traditional one. Any such ambiguity $\chi^2$ makes use of the filtered output of the template bank, thus adding negligible cost to the overall search. We test the performance of ambiguity $\chi^2$ on simulated data using spinless TaylorF2 waveforms. We show that the ambiguity $\chi^2$ essentially gives a clean separation between glitches and signals. Finally, we investigate the effects of mismatch between signal and templates on the $\chi^2$ and also further indicate how the ambiguity $\chi^2$ can be generalized to detector networks for coherent observations.Comment: 21 pages, 5 figure, abstract is shortened to comply with the arXiv's 1920 characters limitation, v2: accepted for publication in PR