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20120105BuchA Donsker Theorem for Lévy Measures Nickl, Richard; Reiß, MarkusGiven n equidistant realisations of a Lévy process (Lt; t >= 0), a natural estimator for the distribution function N of the Lévy measure is constructed. Under a polynomial decay restriction on the characteristic function, ...

20051020BuchA Note on Optimal Stopping in Models with Delay Gapeev, Pavel V.; Reiß, MarkusWe consider an optimal stopping problem in a certain model described by a stochastic delay differential equation. We reduce the initial problem to a freeboundary problem of parabolic type and prove the corresponding ...

20051013BuchAdaptive estimation for affine stochastic delay differential equations Reiß, Markus

20020514BuchAdaptive wavelet Galerkin methods for linear inverse problems Cohen, Albert; Hoffmann, Marc; Reiß, Markus

20050210BuchAn Optimal Stopping Problem in a DiffusionType Model with Delay Gapeev, Pavel V.; Reiß, MarkusWe present an explicit solution to an optimal stopping problem in a model described by a stochastic delay differential equation with an exponential delay measure. The method of proof is based on reducing the initial problem ...

20110530BuchAsymptotic equivalence and sufficiency for volatility estimation under microstructure noise Reiß, MarkusThe basic model for highfrequency data in finance is considered, where an efficient price process is observed under microstructure noise. It is shown that this nonparametric model is in Le Cam's sense asymptotically ...

20051102BuchDelay differential equations driven by Lévy processes: stationarity and Feller properties Reiß, Markus; Riedle, Markus; Gaans, Onno vanWe consider a stochastic delay differential equation driven by a general Lévy process. Both, the drift and the noise term may depend on the past, but only the drift term is assumed to be linear. We show that the segment ...

20110920BuchEstimation of the characteristics of a Lévy process observed at arbitrary frequency Kappus, Johanna; Reiß, Markus

20110530BuchEstimation of the characteristics of a Lévy process observed at arbitrary frequency Kappus, Johanna; Reiß, MarkusA Lévy process is observed at time points of distance Δ until time T. We construct an estimator of the LévyKhinchine characteristics of the process and derive optimal rates of convergence simultaneously in T and Δ. Thereby, ...

20100204BuchEstimation of the characteristics of a Lévy process observed at arbitrary frequency Kappus, Johanna; Reiß, MarkusA Lévy process is observed at time points of distance delta until time T. We construct an estimator of the LévyKhinchine characteristics of the process and derive optimal rates of convergence simultaneously in T and delta. ...

20000907BuchMinimax rates for nonparametric estimation of the drift functional in affine stochastic delay equations Reiß, Markus

20020213DissertationNonparametric estimation for stochastic delay differential equations Reiß, MarkusSei (X(t), t>= r) ein stationärer stochastischer Prozess, der die affine stochastische Differentialgleichung mit Gedächtnis dX(t)=L(X(t+s))dt+sigma dW(t), t>= 0, löst, wobei sigma>0, (W(t), t>=0) eine StandardBrownsche ...

20020625BuchNonparametric estimation of scalar diffusions based on low frequency data is illposed Gobet, Emmanuel; Hoffmann, Marc; Reiß, Markus

20140310BuchNonparametric Test fora Constant Beta over aFixed Time Interval Reiß, Markus; Todorov, Viktor; Tauchen, GeorgeWe derive a nonparametric test for constant (continuous) beta over a fixed interval of time. Continuous beta is defined as the ratio of the continuous covariation between an asset and observable risk factor (e.g., the ...

20050101BuchOn Émery's inequality and a variationofconstants formula Riedle, Markus; Reiß, Markus; Gaans, Onno vanA generalization of Émery's inequality for stochastic integrals is shown for convolution integrals with respect to an arbitrary semimartingale. The inequality is used to prove existence and uniqueness of solutions of ...

20110530BuchPointwise adaptive estimation for quantile regression Reiß, Markus; Rozenholc, Yves; Cuenod, Charles A.A nonparametric procedure for quantile regression, or more generally nonparametric Mestimation, is proposed which is completely datadriven and adapts locally to the regularity of the regression function. This is achieved ...

20060427BuchSpectral calibration of exponential Lévy Models [1] Belomestny, Denis; Reiß, MarkusWe investigate the problem of calibrating an exponential Lévy model based on market prices of vanilla options. We show that this inverse problem is in general severely illposed and we derive exact minimax rates of ...

20060428BuchSpectral calibration of exponential Lévy Models [2] Belomestny, Denis; Reiß, MarkusThe calibration of financial models has become rather important topic in recent years mainly because of the need to price increasingly complex options in a consistent way. The choice of the underlying model is crucial for ...

20111207BuchSpectral estimation of covolatility from noisy observations using local weights Bibinger, Markus; Reiß, MarkusWe propose localized spectral estimators for the quadratic covariation and the spot covolatility of diffusion processes which are observed discretely with additive observation noise. The eligibility of this approach to ...

20030408BuchTransitional Dynamics in the UzawaLucas Model of Endogenous Growth Bethmann, Dirk; Reiß, MarkusWe introduce an easy way of analyzing the transitional dynamics of the UzawaLucas endogenous growth model. We use the value function approach to solve both the social planner’s optimization problem and the representative ...