10,337 research outputs found

    Risk and Volatility: Econometric Models and Financial Practice

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    The advantage of knowing about risks is that we can change our behavior to avoid them. Of course, it is easily observed that to avoid all risks would be impossible; it might entail no flying, no driving, no walking, eating and drinking only healthy foods and never being touched by sunshine. Even a bath could be dangerous. I could not receive this prize if I sought to avoid all risks. There are some risks we choose to take because the benefits from taking them exceed the possible costs. Optimal behavior takes risks that are worthwhile. This is the central paradigm of finance; we must take risks to achieve rewards but not all risks are equally rewarded. Both the risks and the rewards are in the future, so it is the expectation of loss that is balanced against the expectation of reward. Thus we optimize our behavior, and in particular our portfolio, to maximize rewards and minimize risks.time series;

    Bootstrap Markov chain Monte Carlo and optimal solutions for the Law of Categorical Judgment (Corrected)

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    A novel procedure is described for accelerating the convergence of Markov chain Monte Carlo computations. The algorithm uses an adaptive bootstrap technique to generate candidate steps in the Markov Chain. It is efficient for symmetric, convex probability distributions, similar to multivariate Gaussians, and it can be used for Bayesian estimation or for obtaining maximum likelihood solutions with confidence limits. As a test case, the Law of Categorical Judgment (Corrected) was fitted with the algorithm to data sets from simulated rating scale experiments. The correct parameters were recovered from practical-sized data sets simulated for Full Signal Detection Theory and its special cases of standard Signal Detection Theory and Complementary Signal Detection Theory

    Convex Relaxations for Permutation Problems

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    Seriation seeks to reconstruct a linear order between variables using unsorted, pairwise similarity information. It has direct applications in archeology and shotgun gene sequencing for example. We write seriation as an optimization problem by proving the equivalence between the seriation and combinatorial 2-SUM problems on similarity matrices (2-SUM is a quadratic minimization problem over permutations). The seriation problem can be solved exactly by a spectral algorithm in the noiseless case and we derive several convex relaxations for 2-SUM to improve the robustness of seriation solutions in noisy settings. These convex relaxations also allow us to impose structural constraints on the solution, hence solve semi-supervised seriation problems. We derive new approximation bounds for some of these relaxations and present numerical experiments on archeological data, Markov chains and DNA assembly from shotgun gene sequencing data.Comment: Final journal version, a few typos and references fixe

    Multimodal Circular Filtering Using Fourier Series

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    Recursive filtering with multimodal likelihoods and transition densities on periodic manifolds is, despite the compact domain, still an open problem. We propose a novel filter for the circular case that performs well compared to other state-of-the-art filters adopted from linear domains. The filter uses a limited number of Fourier coefficients of the square root of the density. This representation is preserved throughout filter and prediction steps and allows obtaining a valid density at any point in time. Additionally, analytic formulae for calculating Fourier coefficients of the square root of some common circular densities are provided. In our evaluation, we show that this new filter performs well in both unimodal and multimodal scenarios while requiring only a reasonable number of coefficients

    Future state maximisation as an intrinsic motivation for decision making

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    The concept of an “intrinsic motivation" is used in the psychology literature to distinguish between behaviour which is motivated by the expectation of an immediate, quantifiable reward (“extrinsic motivation") and behaviour which arises because it is inherently useful, interesting or enjoyable. Examples of the latter can include curiosity driven behaviour such as exploration and the accumulation of knowledge, as well as developing skills that might not be immediately useful but that have the potential to be re-used in a variety of different future situations. In this thesis, we examine a candidate for an intrinsic motivation with wide-ranging applicability which we refer to as “future state maximisation". Loosely speaking this is the idea that, taking everything else to be equal, decisions should be made so as to maximally keep one's options open, or to give the maximal amount of control over what one can potentially do in the future. Our goal is to study how this principle can be applied in a quantitative manner, as well as identifying examples of systems where doing so could be useful in either explaining or generating behaviour. We consider a number of examples, however our primary application is to a model of collective motion in which we consider a group of agents equipped with simple visual sensors, moving around in two dimensions. In this model, agents aim to make decisions about how to move so as to maximise the amount of control they have over the potential visual states that they can access in the future. We find that with each agent following this simple, low-level motivational principle a swarm spontaneously emerges in which the agents exhibit rich collective behaviour, remaining cohesive and highly-aligned. Remarkably, the emergent swarm also shares a number of features which are observed in real flocks of starlings, including scale free correlations and marginal opacity. We go on to explore how the model can be developed to allow us to manipulate and control the swarm, as well as looking at heuristics which are able to mimic future state maximisation whilst requiring significantly less computation, and so which could plausibly operate under animal cognition

    Topics in exact precision mathematical programming

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    The focus of this dissertation is the advancement of theory and computation related to exact precision mathematical programming. Optimization software based on floating-point arithmetic can return suboptimal or incorrect resulting because of round-off errors or the use of numerical tolerances. Exact or correct results are necessary for some applications. Implementing software entirely in rational arithmetic can be prohibitively slow. A viable alternative is the use of hybrid methods that use fast numerical computation to obtain approximate results that are then verified or corrected with safe or exact computation. We study fast methods for sparse exact rational linear algebra, which arises as a bottleneck when solving linear programming problems exactly. Output sensitive methods for exact linear algebra are studied. Finally, a new method for computing valid linear programming bounds is introduced and proven effective as a subroutine for solving mixed-integer linear programming problems exactly. Extensive computational results are presented for each topic.Ph.D.Committee Chair: Dr. William J. Cook; Committee Member: Dr. George Nemhauser; Committee Member: Dr. Robin Thomas; Committee Member: Dr. Santanu Dey; Committee Member: Dr. Shabbir Ahmed; Committee Member: Dr. Zonghao G
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