No description available.

Diss. Nr. 2928 Wirtschaftswiss. St. Gallen, 2004. / Literaturverz.

No description available.

Paprastai išlikimo teorijoje yra įvertinama integralinė rizikos greičio funkcija, t.y. neparametrinis įvertinimas. Mūsų darbas buvo suparametrizuoti tą funkciją ir įvertinti nežinomus parametrus, ištiriant tų įverčių asimptotines savybes. Ištirti tipiškiausi atvejai. / Usually in the theory of survival of an integrated risk assessment is a function of speed, ie nonparametric assessment. Our work has been suparametrizuoti the function and evaluate the unknown parameters, by examining the asymptotic properties of estimates. Typical cases to investigate.

In this thesis, two methods for assessing the functional form of covariates in the Cox proportional hazards model are evaluated. The methods include one graphical check based on martingale residuals and one graphical check, together with a Kolmogorov-type supremum test, based on cumulative sums of martingale residuals. The methods are evaluated in a simulation study under five different covariate misspecifications with varying sample sizes and censoring degrees. The results from both methods indicate that the type of covariate misspecification, sample size and censoring degree affect the ability to detect and identify the misspecification. The procedure based on smoothed scatterplots of martingale residuals reveals difficulties with assessing whether the behaviour of the smoothed curve in the plot is an indication of a misspecification or a phenomenon that can occur in a correctly specified model. The graphical check together with the test procedure based on cumulative sums of martingale residuals is shown to successfully detect and identify three out of five covariate misspecifications for large sample sizes. For small sample sizes, especially combined with a high censoring degree, the power of the supremum test is low for all covariate misspecifications.

In many clinical studies, continuous variables such as age, blood pressure and cholesterol are measured and analyzed. Often clinicians prefer to categorize these continuous variables into different groups, such as low and high risk groups. The goal of this work is to find the cutpoint of a continuous variable where the transition occurs from low to high risk group. Different methods have been published in literature to find such a cutpoint. We extended the methods of Contal and O’Quigley (1999) which was based on the log-rank test and the methods of Klein and Wu (2004) which was based on the Score test to find the cutpoint of a continuous covariate. Since the log-rank test is a nonparametric method and the Score test is a parametric method, we are interested to see if an extension of the parametric procedure performs better when the distribution of a population is known. We have developed a method that uses the parametric score residuals to find the cutpoint. The performance of the proposed method will be compared with the existing methods developed by Contal and O’Quigley and Klein and Wu by estimating the bias and mean square error of the estimated cutpoints for different scenarios in simulated data.

<p>In this thesis we consider two models for the computation of option prices. The first one is a generalization of the Black-Scholes model. In this generalization the volatility Sigma is not a constant. In the simplest case it changes at once at a certain time moment Tau. In some sense this is the conditionally Levy model. For this generalized Black-Scholes model have been theoretically obtained formulas for vanilla Call/Put option prices. Under the assumption of a good prediction of the parameter Sigma the obtained numerical results fit the real dara better than standard Black-Scholes model.</p><p>Second model is an exponential Levy model, where a Levy process is the CGMY process. We use the finite-difference scheme for computations of option prices. As example we consider vanilla Call/Put, Double-Barrier and Up-and-out options. After the estimation of the parameters of the CGMY process by the method of moments we obtain options prices and calculate fitting error. This fitting error for the CGMY model is smaller than for the Black-Scholes model.</p>

In this thesis we consider two models for the computation of option prices. The first one is a generalization of the Black-Scholes model. In this generalization the volatility Sigma is not a constant. In the simplest case it changes at once at a certain time moment Tau. In some sense this is the conditionally Levy model. For this generalized Black-Scholes model have been theoretically obtained formulas for vanilla Call/Put option prices. Under the assumption of a good prediction of the parameter Sigma the obtained numerical results fit the real dara better than standard Black-Scholes model. Second model is an exponential Levy model, where a Levy process is the CGMY process. We use the finite-difference scheme for computations of option prices. As example we consider vanilla Call/Put, Double-Barrier and Up-and-out options. After the estimation of the parameters of the CGMY process by the method of moments we obtain options prices and calculate fitting error. This fitting error for the CGMY model is smaller than for the Black-Scholes model.

Cette thèse décrit des méthodes de construction de martingales avec marginales spécifiées. La première collection de méthodes procède par quantization. C'est-à-dire en approximant une mesure par une autre mesure dont le support consiste en un nombre fini de points. Nous introduisons une méthode de quantization qui préserve l'ordre convexe. L'ordre convexe est un ordre partiel sur l'espace des mesures qui les compare en termes de leur dispertion relative. Cette nouvelle méthode de quantization présente l'avantage que si deux mesures admettent une transition de martingale alors les mesures quantisées en admettent aussi. Ceci n'est pas le cas pour la méthode de quantization habituellement utilisée en probabilités (la méthode de quantization L2). Pour les mesures quantifiés nous présentons plusieurs méthodes de construction de transition de martingale. La première méthode procède par programmation linéaire. La deuxième méthode procède par construction de matrices avec diagonale et spectre données. La troisième méthode procède par l'algorithme de Chacon et Walsh. Dans une seconde partie la thèse présente une nouvelle solution au problème du plongement de Skorokhod. Dans une troisième partie la thèse étudie la construction de martingales à temps continu avec marginales données. Des constructions sont données à l'aide du draps Brownien. D'autres constructions sont données en modifiant une méthode développée par Albin, les martingales construites ainsi possèdent une propriété de scaling.. Dans une partie annexe, certaines conséquences de cette théorie concernant le management du risque des options asiatiques, par rapport à leur sensibilité à la volatilité et à la maturité sont établies.

It is common practice to use Cox-Snell residuals to check for overall goodness of tin survival models. We evaluate the presumed relation of unit exponentially dis-tributed residuals for a good model t and evaluate under some violations of themodel. This is done graphically with the usual graphs of Cox-Snell residual andformally using Kolmogorov-Smirnov goodness of t test. It is observed that residu-als from a correctly tted model follow unit exponential distribution. However, theCox-Snell residuals do not seem to be sensitive to the violations of the model.