A continuous-outcome expected utility model is presented that generalizes the expected utility theory of Bueno de Mesquita. An examination of the more general model uncovers several unstated assumptions within and produces new conclusions from, while supporting the basic logic of, the expected utility theory. Among the new conclusions is the finding that nations shifting their level of acceptable outcomes to a conflict upward or downward after fighting starts is perfectly consistent with a rational model. The derivations demonstrate the value of theoretical articulation, a task too often neglected in quantitative international relations, and provide a sound logical basis for the construction of systemic theories based upon the expected utility theory.
We propose a novel approach to optimize Partially Observable Markov Decisions Processes (POMDPs) defined on continuous spaces. To date, most algorithms for model-based POMDPs are restricted to discrete states, actions, and observations, but many real-world problems such as, for instance, robot navigation, are naturally defined on continuous spaces. In this work, we demonstrate that the value function for continuous POMDPs is convex in the beliefs over continuous state spaces, and piecewise-linear convex for the particular case of discrete observations and actions but still continuous states. We also demonstrate that continuous Bellman backups are contracting and isotonic ensuring the monotonic convergence of value-iteration algorithms. Relying on those properties, we extend the PERSEUS algorithm, originally developed for discrete POMDPs, to work in continuous state spaces by representing the observation, transition, and reward models using Gaussian mixtures, and the beliefs using Gaussian mixtures or particle sets. With these representations, the integrals that appear in the Bellman backup can be computed in closed form and, therefore, the algorithm is computationally feasible. Finally, we further extend PERSEUS to deal with continuous action and observation sets by designing effective sampling approaches. ; This work was supported by the project 'Perception, action & cognition through learning of object-action complexes.' (4915). Josep M. Porta has been partially supported by a Ramón y Cajal contract from the Spanish government and by the EU PACO-PLUS Project FP6-2004-IST-4-27657. Nikos Vlassis and Matthijs Spaan are supported by PROGRESS, the embedded systems research program of the Dutch organization for Scientific Research NWO, the Dutch Ministry of Economic Affairs and the Technology Foundation STW, project AES5414. Pascal Poupart is supported by the Canada's National Science and Engineering Research Council. ; Peer Reviewed
Der Value at Risk ist die am stärksten verbreitete Kennzahl zur Bestimmung des Risikos bei Finanzinstituten. Für diese gibt es bezüglich Theorie, Simulation und empirischer Anwendung bereits ein breites Spektrum an Literatur. Im Rahmen dieser Arbeit werden verschiedene Methoden zur Schätzung des Value at Risk gegenübergestellt und bezüglich ihrer Performance untereinander verglichen. Zusätzlich zum Value at Risk wird der Expected Shortfall als mögliche Alternative aufgeführt. Der wesentliche Fokus liegt zum einen auf dem Vergleich von bedingten Methoden mit und ohne vorherige Filterung von Daten. Zum anderen soll die Frage beantwortet werden, ob bedingte oder unbedingte Methoden für die Schätzung der Risikomaße zu favorisieren sind. Auf Basis der in dieser Arbeit durchgeführten Simulations- und empirischen Studien wird gezeigt, dass die Filterung von Daten einen nicht zu verachtenden Mehrwert erzielt. Nach einer adäquaten Filterung liefern sowohl Extremwertmodelle als auch nichtparametrische Modelle gute Ergebnisse. In der empirischen Studie stellen sich die bedingten Methoden als vorteilhaft heraus.
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In this book Simona Roccioletti reviews several valuable studies about risk measures and their properties; in particular she studies the new (and heavily discussed) property of "Elicitability" of a risk measure. More important, she investigates the issue related to the backtesting of Expected Shortfall. The main contribution of the work is the application of "Test 1" and "Test 2" developed by Acerbi and Szekely (2014) on different models and for five global market indexes. Contents Risk measures and their properties Elicitability Backtesting (VaR and ES) Empirical Analysis MATLAB code Target Groups Researchers and Students in Economics and Finance Practitioners in Risk Management The Author Simona Roccioletti obtained her Master of Arts degree in Quantitative Asset and Risk Management at the University of Applied Sciences (bfi) Vienna, Austria.
