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20060202BuchA Note on Limit Theorems for Multivariate Martingales Küchler, Uwe; Sørensen, MichaelMultivariate versions of the law of large numbers and the central limit theorem for martingales are given in a generality that is often necessary when studying statistical inference for stochastic process models. To ...

20060101BuchBilateral Gamma Distributions and Processes in Financial Mathematics Küchler, Uwe; Tappe, StefanWe present a class of Lévy processes for modelling financial market fluctuations: Bilateral Gamma processes. Our starting point is to explore the properties of bilateral Gamma distributions, and then we turn to their ...

19990902BuchCoherent Risk Measures, Valuation Bounds, and (My,p)Portfolio Optimization Jaschke, Stefan R.; Küchler, Uwe

20060202BuchDelay Estimation for some Stationary Diffusiontype processes Küchler, Uwe; Kutoyants, Yury A.In this paper the asymptotic behaviour of the maximum likelihood and Bayesian estimators of a delay parameter is studied. The observed process is supposed to be the solution of a linear stochastic differential equation ...

20051012BuchMarkovian short rates in a forward rate model with ageneral class of Lévy processes Küchler, Uwe; Naumann, EvaShort rates of interest are considered within in the term structure model of EberleinRaible [6] driven by a Lévy process. It is shown that they are Markovian if and only if the volatility function factorizes. This extends ...

20110920BuchMinimal Entropy Martingale Measure for Lévy Processes Krol, Katja; Küchler, UweLet X be a realvalued Lévy process under P in its natural filtration. The minimal entropy martingale measure is defined as an absolutely continuous martingale measure that minimizes the relative entropy with respect to ...

20110920BuchOn guaranteed parameter estimation of a multiparameter linear regression process Küchler, Uwe; Vasiliev, Vyacheslav A.

20010223BuchOn guaranteed parameter estimation of stochastic differential equations with time delay by noisy observations Küchler, Uwe; Vasiliev, Vjatscheslav A.

20051013BuchOn integrals with respect to Lévy processes Küchler, Uwe

20051020BuchOn Large Deviations in Testing OrnsteinUhlenbeck Type Models with Delay Gapeev, Pavel V.; Küchler, UweWe obtain an explicit form of fine large deviation theorems for the loglikelihood ratio in testing models with observed OrnsteinUhlenbeck processes and get explicit rates of decrease for error probabilities of NeymanPearson, ...

20051021BuchOn lifetimedistributions of some onedimensional diffusions and related exponential families Küchler, UweDiffusions X on the positive halfaxis with elastic killing boundary at zero and inaccessible boundary at ∞ are considered. The lifetime ζ is finite and hθ(x) = Ex exp(θζ), n ≥ 0, is an θexcessive function. The h(θ)transforms ...

20051020BuchOn Markovian Short Rates in Term Structure Models Driven by JumpDiffusion Processes Gapeev, Pavel V.; Küchler, UweWe study a bond market model and related term structure of interest rates where prices of zero coupon bonds are driven by a jumpdiffusion process. We present a criterion on the deterministic forward rate volatilities under ...

20051012BuchOn oscillations of the geometric Brownian motion with time delayed drift Gushchin, Alexander A.; Küchler, Uwe

20060802BuchOn parameter estimation of stochastic delay differential equations with guaranteed accuracy by noisy observations Küchler, Uwe; Vasiliev, Vjatscheslav A.Let (X(t), t ≥ −1) and (Y (t), t ≥ 0) be stochastic processes satisfying dX(t) = aX(t)dt + bX(t − 1)dt + dW(t) and dY (t) = X(t)dt + dV (t), respectively. Here (W(t), t ≥ 0) and (V (t), t ≥ 0) are independent standard ...

20011108BuchOn parametric statistical models for stationary solutions of affine stochastic delay differential equations Gushchin, Alexander A.; Küchler, Uwe

19981103BuchOn sequential parameter estimation for some linear stochastic differential equations with time delay Küchler, Uwe; Vasiliev, Vjatscheslav A.

19981124BuchOn Stationary Solutions of Delay Differential Equations Driven by a Lévy Process Gushchin, Alexander A.; Küchler, Uwe

20090702BuchStatistical inference for discretetime samples from affine stochastic delay differential equations Küchler, Uwe; Sørensen, MichaelStatistical inference for discrete time observations of an affine stochastic delay differential equation is considered. The main focus is on maximum pseudolikelihood estimators, which are easy to calculate in practice. ...

20010402BuchÜber die Stabilität des EulerSchemas für eine Affine Stochastische Differentialgleichung mit Gedächtnis Gilsing, Hagen; Küchler, Uwe; Platen, Eckhard

20010308BuchWeak Discrete Time Approximation of Stochastic Differential Equations with Time Delay Küchler, Uwe; Platen, Eckhard