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作者：Frydman, H; Lakner, P
作者单位：New York University
摘要：We consider the process dY(t) = u(t) dt + dW(t), where u is a process not necessarily adapted to F-Y (the filtration generated by the process Y) and W is a Brownian motion. We obtain a general representation for the likelihood ratio of the law of the Y process relative to Brownian measure. This representation involves only one basic filter (expectation of u conditional on observed process Y). This generalizes the result of Kailath and Zakai [Ann. Math. Statist. 42 (1971) 130-140] where it is a...
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作者：Kontoyiannis, I; Meyn, SP
作者单位：Brown University; Brown University; University of Illinois System; University of Illinois Urbana-Champaign; University of Illinois System; University of Illinois Urbana-Champaign
摘要：Consider the partial sums {S-t} of a real-valued functional F(phi)(t)) of a Markov chain {(phi(t)} with values in a general state space. Assuming only that the Markov chain is geometrically ergodic and that the functional F is bounded, the following conclusions are obtained: Spectral theory. Well-behaved solutions f can be constructed for the multiplicative Poisson equation (e(alphaF) P)f =lambdaf, where P is the transition kernel of the Markov chain and alpha is an element of C is a constant....
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作者：Kurkova, IA; Suhov, YM
作者单位：Sorbonne Universite; University of Cambridge; University of Cambridge
摘要：Malyshev's theory of asymptotics of stationary probabilities for a random walk in a quarter-plane is extended to cover the case of join-the-shorter-queues.
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作者：Gaier, J; Grandits, P; Schachermayer, W
作者单位：Technische Universitat Wien
摘要：We study the infinite time ruin probability for an insurance company in the classical Cramer-Lundberg model with finite exponential moments. The additional nonclassical feature is that the company is also allowed to invest in some stock market, modeled by geometric Brownian motion. We obtain an exact analogue of the classical estimate for the ruin probability without investment, that is, an exponential inequality. The exponent is larger than the one obtained without investment, the classical L...
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作者：Duffy, K; Lewis, JT; Sullivan, WG
作者单位：Technological University Dublin
摘要：Logarithmic asymptotics are proved for the tail of the supremum of a stochastic process, under the assumption that the process satisfies a restricted large deviation principle on regularly varying scales. The formula for the rate of decay of the tail of the supremum, in terms of the underlying rate function, agrees with that stated by Duffield and O'Connell [Math. Proc. Cambridge Philos. Soc. (1995) 118 363-374]. The rate function of the process is not assumed to be convex. A number of queuein...
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作者：Bruss, FT; Grübel, R
作者单位：Universite Libre de Bruxelles; Leibniz University Hannover
摘要：Let M-n be the maximum of a sample X-1,..., X-n from a discrete distribution and let W-n be the number of i's, 1 less than or equal to i less than or equal to n, such that X-i = M-n. We discuss the asymptotic behavior of the distribution of Wn as n --> infinity. The probability that the maximum is unique is of interest in diverse problems, for example, in connection with an algorithm for selecting a winner, and has been studied by several authors using mainly analytic tools. We present here an...
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作者：Lamberton, D; Villeneuve, S
作者单位：Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite PSL; Ecole des Hautes Etudes en Sciences Sociales (EHESS); Universite de Toulouse; Universite Toulouse 1 Capitole; Centre National de la Recherche Scientifique (CNRS)
摘要：We study the behavior of the critical price of an American put option near maturity when the underlying stock pays dividends at a continuous rate. The results also apply to foreign currencies American options.
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作者：Jakubenas, P; Levental, S; Ryznar, M
作者单位：Sorbonne Universite; Universite Paris Cite; Michigan State University; Wroclaw University of Science & Technology
摘要：We study the minimal investment that is needed in order to super-replicate (i.e., hedge with certainty) continuous-time options under transaction costs. We deal with both exotic and path-independent European and American options. In all our examples we prove that the optimal strategy is the cheapest possible buy and hold. Our method is to study the problem in a discrete-time shadow market that is free of transaction costs where the options are perpetual. We also produce useful and precise esti...
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作者：Embrechts, P; Samorodnitsky, G
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; Cornell University
摘要：The recent increasing interplay between actuarial and financial mathematics has led to a surge in risk theoretic modeling. Especially actuarial ruin models under fairly general conditions on the underlying risk process have become a focus of attention. Motivated by applications such as the modeling of operational risk losses in financial risk management, we investigate the stability of classical asymptotic ruin estimates when claims are heavy, and this under variability of the claim intensity ...
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作者：Mahmoud, HM; Neininger, R
作者单位：George Washington University; McGill University
摘要：We investigate random distances in a random binary search tree. Two types of random distance are considered: the depth of a node randomly selected from the tree, and distance between randomly selected pairs of nodes. By a combination of classical methods and modern contraction techniques we arrive at a Gaussian limit law for normed random distances between pairs. The exact forms of the mean and variance of this latter distance are first derived by classical methods to determine the scaling pro...
