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作者：Zucca, Cristina; Sacerdote, Laura
作者单位：University of Turin
摘要：The inverse first-passage problem for a Wiener process (W(t))(t >= 0) seeks to determine a function b : R(+) -> R such that tau = inf{t > 0 vertical bar W(t) >= b(t)} has a given law. In this paper two methods for approximating the unknown function b are presented. The errors of the two methods are studied. A set of examples illustrates the methods. Possible applications are enlighted.
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作者：Blanchet, Jose H.
作者单位：Columbia University
摘要：Importance sampling has been reported to produce algorithms with excellent empirical performance in counting problems. However, the theoretical support for its efficiency in these applications has been very limited. In this paper, we propose a methodology that can be used to design efficient importance sampling algorithms for counting and test their efficiency rigorously. We apply our techniques after transforming the problem into a rare-event simulation problem-thereby connecting complexity a...
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作者：Dolera, Emanuele; Gabetta, Ester; Regazzini, Eugenio
作者单位：University of Pavia
摘要：Let f (.,t) be the probability density function which represents the solution of Kac's equation at time t, with initial data f(0), and let g(sigma) be the Gaussian density with zero mean and variance sigma(2), sigma(2) being the value of the second moment of f(0). This is the first study which proves that the total variation distance between f(., t) and g(sigma) goes to zero, as t ->+infinity, with an exponential rate equal to -1/4. In the present paper, this fact is proved on the sole assumpt...
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作者：Pra, Paolo Dai; Runggaldier, Wolfgang J.; Sartori, Elena; Tolotti, Marco
作者单位：University of Padua; Bocconi University; Scuola Normale Superiore di Pisa; Universita Ca Foscari Venezia
摘要：Using particle system methodologies we study the propagation of financial distress in a network of firms facing credit risk, We investigate the phenomenon of a credit crisis and quantify the losses that a bank may suffer in a large credit portfolio. Applying a large deviation principle we compute the limiting distributions of the system and determine the time evolution of the credit quality indicators of the firms, deriving moreover the dynamics of a global financial health indicator. We final...
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作者：Hitczenko, Pawel; Wesolowski, Jacek
作者单位：Drexel University; Warsaw University of Technology
摘要：We consider the tail behavior of random variables R which are solutions of the distributional equation R (d)= Q + M R, where (Q. M) is independent of R and vertical bar M vertical bar <= 1. Goldie and Grubel showed that the tails of R are no heavier than exponential and that if Q is bounded and M resembles near I the uniform distribution, then the tails of R are Poissonian. In this paper, we further investigate the connection between the tails of R and the behavior of M near 1. We focus on the...
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作者：Gamarnik, David; Katz, Dmitriy
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
摘要：One of the basic properties of a queueing network is stability. Roughly speaking, it is the property that the total number of jobs in the network remains bounded as a function of time. One of the key questions related to the stability issue is how to determine the exact conditions under which a given queueing network operating under a given scheduling policy remains stable. While there was much initial progress in addressing this question, most of the results obtained were partial at best and ...
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作者：Collamore, Jeffrey F.
作者单位：University of Copenhagen
摘要：We develop sharp large deviation asymptotics for the probability of ruin in a Markov-dependent stochastic economic environment and study the extremes for some related Markovian processes which arise in financial and insurance mathematics, related to perpetuities and the ARCH(I) and GARCH(1,1) time series models. Our results build upon work of Goldie [Ann. Appl. Probab. 1 (1991) 126-166], who has developed tail asymptotics applicable for independent sequences of random variables subject to a ra...
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作者：Mayberry, John
作者单位：Cornell University
摘要：In this work, we examine spectral properties of Markov transition operators corresponding to Gaussian perturbations of discrete time dynamical systems on the circle. We develop a method for calculating asymptotic expressions for eigenvalues (in the zero noise limit) and show that changes to the number or period of stable orbits for the deterministic system correspond to changes in the number of limiting modulus 1 eigenvalues of the transition operator for the perturbed process. We call this ph...
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作者：Gruebel, Rudolf
作者单位：Leibniz University Hannover
摘要：A zero-one sequence describes a path through a rooted directed binary tree T; it also encodes a real number in [0, 1]. We regard the level of the external node of T along the path as a function on the unit interval, the silhouette of T. We investigate the asymptotic behavior of the resulting stochastic processes for sequences of trees that are generated by the binary search tree algorithm.
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作者：Ait-Sahalia, Yacine; Cacho-Diaz, Julio; Hurd, T. R.
作者单位：Princeton University; National Bureau of Economic Research; McMaster University
摘要：We analyze the consumption-portfolio selection problem of an investor facing both Brownian and jump risks. We bring new tools, in the form of orthogonal decompositions, to bear on the problem in order to determine the optimal portfolio in closed form. We show that the optimal policy is for the investor to focus on controlling his exposure to the jump risk, while exploiting differences in the Brownian risk of the asset returns that lies in the orthogonal space.
