In practice, baffle blocks and sills are commonly being used to stabilize the location of a hydraulic jump and shorten the length of a stilling basin. On the other hand, gravels, corrugations and rectangular prismatic roughnesses which cover the entire length of the basin or placed in a staggered manner may be an alternative. The objective of this study is to determine the effects of these roughness elements on the characteristics of hydraulic jumps such as conjugate depth, jump length and energy dissipation using experimental data collected from the previous studies. The investigations show that the roughness elements have positive effects on the characteristics of hydraulic jumps. The tailwater depth reduction compared to classical jump is 2-10%. The length of the jump is reduced about by 30-50% by prismatic roughness elements, 40% by corrugations, and 30% by gravels. The roughness elements induce 3-15% more energy dissipation than that of classical jump. Therefore, these types of bed roughness elements should be considered as an effective alternative of accessory devices such as baffle blocks and sills.

A study of the hydraulic jump on a trapezoidal prismatic channel and roughened beds is presented. Extensive measurements have been made regarding the characteristics of hydraulic jumps as sequent depths, wing fluctuations, energy dissipation and jump length on artificially roughened beds for Froude numbers between 4.16 and 14.58. Three different types of prismatic roughness elements and nine different roughness patterns were installed separately on channel bottom and side walls throughout the experiments to obtain rough surfaces. Strip roughness elements were built from fiberglass sheets and implemented perpendicular to the flow direction. To avoid cavitation, roughness elements were designed in that way that the crests of the elements are not protruding into the flow. The founded properties were compared with the available data in literature and with the properties of hydraulic jump occurred on smooth bed.

The main goal of this research is to estimate the model parameters and to detect multiple change points in the long memory parameter of Gaussian ARFIMA(p, d, q) processes. Our approach is Bayesian and inference is done on wavelet domain. Long memory processes have been widely used in many scientific fields such as economics, finance and computer science. Wavelets have a strong connection with these processes. The ability of wavelets to simultaneously localize a process in time and scale domain results in representing many dense variance-covariance matrices of the process in a sparse form. A wavelet-based Bayesian estimation procedure for the parameters of Gaussian ARFIMA(p, d, q) process is proposed. This entails calculating the exact variance-covariance matrix of given ARFIMA(p, d, q) process and transforming them into wavelet domains using two dimensional discrete wavelet transform (DWT2). Metropolis algorithm is used for sampling the model parameters from the posterior distributions. Simulations with different values of the parameters and of the sample size are performed. A real data application to the U.S. GNP data is also reported. Detection and estimation of multiple change points in the long memory parameter is also investigated. The reversible jump MCMC is used for posterior inference. Performances are evaluated on simulated data and on the Nile River dataset.

This dissertation includes two topics. For the first topic about the housing price jump risk, we use EM gradient algorithms to estimate parameters of the jump diffusion model and test whether the US monthly housing price have jump risk during 1986 to 2006. Then, in order to obtain a viable pricing framework of mortgage insurance contracts, this paper uses the jump diffusion processes of Merton (1976) to model the dynamic process of housing price. Using this model, we investigate the impact of price jump risk on the valuation of mortgage insurance premium from jump intensity, abnormal volatility of jump size and normal volatility. Empirical results indicate that the abnormal volatility of jump size has the most significant impact on the mortgage insurance premium. For the second topic about the catastrophe risk, we investigate that, for catastrophic events, the assumption that catastrophe claims occur in terms of the Poisson process seems inadequate as it has constant intensity. We propose Markov Modulated Poisson process to model the arrival process for catastrophic events. Under this process, the underlying state is governed by a homogenous Markov chain, and it is the generalization of Cummins and Geman (1993, 1995), Chang, Chang, and Yu (1996), Geman and Yor (1997) and Vaugirard (2003a, 2003b). We apply Markov jump diffusion model to derive pricing formulas for catastrophe insurance products, included catastrophe futures call option, catastrophe PCS call spread and catastrophe bond. We use the data of PCS index and the annual number of hurricane events during 1950 to 2004 to test the quality of the fitting under the Markov Modulated Poisson process and the Poisson process. We reach the conclusion that the Markov Modulated Poisson process is fitter than the Poisson process and Weiner process in modeling the arrival rate of hurricane events when pricing three insurance products. Hence, if different status of climate environment has significant different arrival intensity in real economy, using jump diffusion model to evaluate CAT insurance products could cause significant mispricing.

The English online auction creates great business opportunities. However, it¡¦s different from traditional English auction in long bidding time, wide area, high risk, massive information, and low switching cost. It makes bidders easy to search information of the goods but difficult to win the auction. The bidders' transaction cost structure has changed from information phase to agreement phase. So, the bidders need more precise supporting tools to help them make decisions. The aim of this research is to investigate two-person optimal bidding strategies under three dimensions of the decision space: the sequence decision (bid firstly or later), the bid decision (bid or quit), and the jump decision (minimum increase or jump bid). It is assumed that there are two bidders competing in one auction. Variables associated with the auction system include the floor price and the minimum increase. Variables associated with the bidders include the private value of the bidding object, and the cost of bid per turn. Strategies were evaluated based on the following criteria: who wins, how many turns to win the bid, the deal price, the utility of the winner and the loser, the probability of winning, and the expected utility. The results indicate that every strategy has its advantages and disadvantages under certain conditions. This research provides guiding rules for the bidders to choose a better strategy.

Diese Arbeit beschäftigt sich mit den in konventionellen Handschaltgetrieben als auch in automatisierten Schaltgetrieben für die Funktion "Schalten/Leistungsfluss herstellen" verwendeten Zahnkupplungen. Einmal eingelegt soll der gewählte Gang bis zur Herausnahme durch den Fahrer den Leistungsfluss gewährleisten. Es gibt aber Getriebe, bei denen sich eine korrekt betätigte Schalteinrichtung während der Fahrt selbsttätig wieder entkoppelt. Mit der vorliegenden Arbeit wird dieses Problem, als „Gangspringen“ bezeichnet, erklärt und analysiert. Das Ergebnis dieser Arbeit sind Vorschläge und Möglichkeiten zur Vermeidung dieser Fehlfunktion.

In this paper, we consider as an inverse problem the simultaneous estimation of the five parameters of a jump diffusion process from return observations of a price trajectory. We show that there occur some ill-posedness phenomena in the parameter estimation problem, because the forward operator fails to be injective and small perturbations in the data may lead to large changes in the solution. We illustrate the instability effect by a numerical case study. To overcome the difficulty coming from ill-posedness we use a multi-parameter regularization approach that finds a trade-off between a least-squares approach based on empircal densities and a fitting of semi-invariants. In this context, a fixed point iteration is proposed that provides good results for the example under consideration in the case study.

Die Dissertation widmet sich dem inversen Problem der Bestimmung der fünf Parameter eines Jump-Diffusions-Prozesses aus einer Preistrajektorie. Numerische Rechnungen zu statistischen Standardverfahren haben gezeigt, dass Stabilitätsprobleme insbesondere dann auftreten, wenn die Parameter aus einer relativ kleinen Zahl beobachteter Assetpreise bestimmt werden. Daher untersuchen wir das Problem der Parameterschätzung in dieser Arbeit unter Einbeziehung von Methoden aus der Theorie inverser Probleme, da deren zentrales Anliegen die Analyse und Regularisierung inkorrekter und instabiler inverser Aufgaben ist. In dieser Arbeit werden Phänomene der Instabilität der Parameterbestimmung herausgearbeitet und analysiert. Hierfür leiten wir eine entsprechende nichtlineare Operatorgleichung her, die den Zusammenhang zwischen einer von den Parametern abhängigen Trajektorie des Jump-Diffusions-Prozesses und der Dichtefunktion der Returns beschreibt. Diese Operatorgleichung untersuchen wir bezüglich ihrer Korrektheit. Wir zeigen anhand einer Fallstudie mit simulierten Daten, dass bei der numerischen Lösung Inkorrektheitsphänomene auftreten, sobald die Daten mit kleinen Datenfehlern behaftet sind. Um diese Stabilitätsprobleme zu überwinden, diskutieren wir einen Multiparameter-Regularisierungszugang, bei dem zusätzlich zur Least-Squares Anpassung der empirischen Dichtefunktion die Semiinvarianten berücksichtigt werden. / This thesis deals with the inverse problem of estimating simultaneously the five parameters of a jump diffusion process based on return observations of a price trajectory. It is well known that there occur instability effects using conventional statistical methods, particularly if only a small number of data are available. Therefore we apply the theory of inverse problems for parameter estimation. We analyse the forward operator mapping the parameters to the density function of the returns with respect to well-posedness and ill-posedness of the problem. We show that there occur some ill-posedness phenomena in the parameter estimation problem in case of noisy data and illustrate the instability effect by a numerical case study. To obtain stable approximate solutions of the estimation problem, we use a multi-parameter regularization approach, where a least-squares fitting of empirical densities is superposed by a quadratic penalty term of fitted semi-invariants with weights.

In this paper we discuss the stable solvability of the inverse problem of parameter identification in a jump diffusion model. Therefore we introduce the forward operator of this inverse problem and analyze its properties. We show continuity of the forward operator and stability of the inverse problem provided that the domain is restricted in a specific manner such that techniques of compact sets can be exploited. Furthermore, we show that there is an asymptotical non-injectivity which causes instability problems whenever the jump intensity increases and the jump heights decay simultaneously.

In this note, we consider an inverse problem in a jump diffusion model. Using characteristic functions we prove the injectivity of the forward operator mapping the five parameters determining the model to the density function of the return distribution.