2003

最新文章

• Volatility time and properties of option prices AI翻译
  作者：Janson, S; Tysk, J
  作者单位：Uppsala University
  摘要：We use a notion of stochastic time, here called volatility time, to show convexity of option prices in the underlying asset if the contract function is convex as well as continuity and monotonicity of the option price in the volatility. The volatility time is obtained as the almost surely unique stopping time solution to a random ordinary differential equation related to volatility. This enables us to write price processes, or processes modeled by local martingales, as Brownian motions with re...
• Limit theorem for Leland's strategy AI翻译
  作者：Pergamenshchikov, S
  作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Rouen Normandie
  摘要：The Leland strategy for an approximate hedging of the call option under transactions costs is studied. The rate of convergence in the Kabanov-Safarian theorem for the Leland strategy is found. The limit theorem for the hedging portfolio is proved.
• Asymptotic results for long memory LARCH sequences AI翻译
  作者：Berkes, I; Horváth, J
  作者单位：HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Hungarian Academy of Sciences; Utah System of Higher Education; University of Utah
  摘要：For a LARCH (linear ARCH) sequence (Y-n, sigma(n),) exhibiting long range dependence, we determine the limiting distribution of sums Sigma f (y(n)), Sigma f (sigma(n)) for smooth functions f satisfying E(y(0)f' (y(0))) = 0, E (sigma(0)f' (sigma(0))) not equal 0. We also give an approximation formula for the above sums, providing the first term of the asymptotic expansions of Sigma f (y(n)), Sigma f (sigma(n)).
• Saddlepoint approximations and nonlinear boundary crossing probabilities of Markov random walks AI翻译
  作者：Chan, HP; Lai, TL
  作者单位：National University of Singapore; Stanford University
  摘要：Saddlepoint approximations are developed for Markov random walks S-n and are used to evaluate the probability that (j - i) g ((S-j - S-i) / (j - i)) exceeds a threshold value for certain sets of (i, j). The special case g(x) = x reduces to the usual scan statistic in change-point detection problems, and many generalized likelihood ratio detection schemes are also of this form with suitably chosen g. We make use of this boundary crossing probability to derive both the asymptotic Gumbel-type dis...
• Rescaled interacting diffusions converge to super Brownian motion AI翻译
  作者：Cox, JT; Klenke, A
  作者单位：Syracuse University; University of Cologne
  摘要：Super Brownian motion is known to occur as the limit of properly rescaled interacting particle systems such as branching random walk, the contact process and the voter model. In this paper we show that certain linearly interacting diffusions converge to super Brownian motion if suitably rescaled in time and space. The results comprise nearest neighbor interaction as well as long range interaction.
• Maximum likelihood estimation of hidden Markov processes AI翻译
  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...
• Spectral theory and limit theorems for geometrically ergodic Markov processes AI翻译
  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....
• Malyshev's theory and JS-queues. Asymptotics of stationary probabilities AI翻译
  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.
• Asymptotic ruin probabilities and optimal investment AI翻译
  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...
• Logarithmic asymptotics for the supremum of a stochastic process AI翻译
  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...