Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 145-151).

A central bank is usually assigned two functions: the control of inflation and the maintenance of a safetybanking sector. What are the precise conditions under which trigger strategies from the private sector can solve the time inconsistency problem and induce the central bank to choose zero inflation under a nonstationary natural rate? Can an optimal contract be used together with reputation forces to implement a desired socially optimal monetary policy rule? How to design a truthtelling contract to control the risk taking behaviors of the bank? My dissertation attempts to deal with these issues using three primary methodologies: monetary economics, game theory and optimal stochastic control theory.

Ill-posed sets of linear equations typically arise when discretizing certain types of integral transforms. A well known example is image reconstruction, which can be modelled using the Radon transform. After expanding the solution into a finite series of basis functions a large, sparse and ill-conditioned linear system arises. We consider the solution of such systems. In particular we study a new class of iteration methods named DROP (for Diagonal Relaxed Orthogonal Projections) constructed for solving both linear equations and linear inequalities. This class can also be viewed, when applied to linear equations, as a generalized Landweber iteration. The method is compared with other iteration methods using test data from a medical application and from electron microscopy. Our theoretical analysis include convergence proofs of the fully-simultaneous DROP algorithm for linear equations without consistency assumptions, and of block-iterative algorithms both for linear equations and linear inequalities, for the consistent case. When applying an iterative solver to an ill-posed set of linear equations the error typically initially decreases but after some iterations (depending on the amount of noise in the data, and the degree of ill-posedness) it starts to increase. This phenomena is called semi-convergence. It is therefore vital to find good stopping rules for the iteration. We describe a class of stopping rules for Landweber type iterations for solving linear inverse problems. The class includes, e.g., the well known discrepancy principle, and also the monotone error rule. We also unify the error analysis of these two methods. The stopping rules depend critically on a certain parameter whose value needs to be specified. A training procedure is therefore introduced for securing robustness. The advantages of using trained rules are demonstrated on examples taken from image reconstruction from projections. / Vi betraktar lösning av sådana linjära ekvationssystem som uppkommer vid diskretisering av inversa problem. Dessa problem karakteriseras av att den sökta informationen inte direkt kan mätas. Ett välkänt exempel utgör datortomografi. Där mäts hur mycket strålning som passerar genom ett föremål som belyses av en strålningskälla vilken intar olika vinklar i förhållande till objektet. Syftet är förstås att generera bilder av föremålets inre (i medicinska tillämpngar av det inre av kroppen). Vi studerar en klass av iterativa lösningsmetoder för lösning av ekvationssystemen. Metoderna tillämpas på testdata från bildrekonstruktion och jämförs med andra föreslagna iterationsmetoder. Vi gör även en konvergensanalys för olika val av metod-parametrar. När man använder en iterativ metod startar man med en begynnelse approximation som sedan gradvis förbättras. Emellertid är inversa problem känsliga även för relativt små fel i uppmätta data. Detta visar sig i att iterationerna först förbättras för att senare försämras. Detta fenomen, s.k. ’semi-convergence’ är väl känt och förklarat. Emellertid innebär detta att det är viktigt att konstruera goda stoppregler. Om man avbryter iterationen för tidigt fås dålig upplösning och om den avbryts för sent fås en oskarp och brusig bild. I avhandligen studeras en klass av stoppregler. Dessa analyseras teoretiskt och testas på mätdata. Speciellt föreslås en inlärningsförfarande där stoppregeln presenteras med data där det korrekra värdet på stopp-indexet är känt. Dessa data används för att bestämma en viktig parameter i regeln. Sedan används regeln för nya okända data. En sådan tränad stoppregel visar sig fungera väl på testdata från bildrekonstruktionsområdet.

Optimal stopping and mathematical finance are intimately connected since the value of an American option is given as the solution to an optimal stopping problem. Such a problem can be viewed as a game in which we are trying to maximize an expected reward. The solution involves finding the best possible strategy, or equivalently, an optimal stopping time for the game. Moreover, the reward corresponding to this optimal time should be determined. It is also of interest to know how the solution depends on the model parameters. For example, when pricing and hedging an American option, the volatility needs to be estimated and it is of great practical importance to know how the price and hedging portfolio are affected by a possible misspecification. The first paper of this thesis investigates the performance of the delta hedging strategy for a class of American options with non-convex payoffs. It turns out that an option writer who overestimates the volatility will obtain a superhedge for the option when using the misspecified hedging portfolio. In the second paper we consider the valuation of a so-called stock loan when the lender is allowed to issue a margin call. We show that the price of such an instrument is equivalent to that of an American down-and-out barrier option with a rebate. The value of this option is determined explicitly together with the optimal repayment strategy of the stock loan. The third paper considers the problem of how to optimally stop a Brownian bridge. A finite horizon optimal stopping problem like this can rarely be solved explicitly. However, one expects the value function and the optimal stopping boundary to satisfy a time-dependent free boundary problem. By assuming a special form of the boundary, we are able to transform this problem into one which does not depend on time and solving this we obtain candidates for the value function and the boundary. Using stochastic calculus we then verify that these indeed satisfy our original problem. In the fourth paper we consider an investor wanting to take advantage of a mispricing in the market by purchasing a bull spread, which is liquidated in case of a market downturn. We show that this can be formulated as an optimal stopping problem which we then, using similar techniques as in the third paper, solve explicitly. In the fifth and final paper we study convexity preservation of option prices in a model with jumps. This is done by finding a sufficient condition for the no-crossing property to hold in a jump-diffusion setting.

This thesis describes the development of computer programs and the theory for the calculations of stopping power and nuclear reaction kinematics. The nuclear reaction kinematics program computes position and nonrelativistic energy data as well as center-of-mass solid angle transformations and information on detector resolution for nuclear reactions and elastic scattering experiments involving two-body final states. The stopping power program calculates stopping power (an index of the charged particle energy absorption properties of a material) of elemental absorbers for protons, deuterons, tritons, He3, and alpha particles from minimal input data. The calculated stopping powers are accurate to within one per cent over the nonrelativistic energy range of 2 to 12 Mev.Ball State UniversityMuncie, IN 47306

The identification of stopping charged particles in G.5 nuclear emulsion by using a residual range ionization method has been investigated in this experiment using a large stack of ILFord, G.5 nuclear emulsion pellicles exposed to 450 and 435 Me V/c K ˉ mesons at the Berkeley Bevatron.The restricted rate of energy loss vs kinetic energy for protons has been calculated theoretically, and given in Barkas(9). Then for given values of B , we calculated the restricted rate of energy loss vs the kinetic energy of muon, pion, kaon, and sigma particles.The measurement of the residual range and the counting of blobs in each residual range segment were carried out for four known stopping pions tracks. A second degree polynomial computer fit program was used to interpret the plot of residual range vs blobs/100 μ m. Then a particular point on the plot was chosen as a reference for normalizing the relative grain density (g*), theoretically and experimentally. Next, theoretical tables of residual range (R) vs relative grain density (g*theo) were calculated for muons, pions, kaons, protons, and sigmas. Those portions of the latter tables, for which (g*theo) was less than - 2, were used for the above mentioned theoretical plot of residual range (R) vs relative grain density (g* theo). The theoretically predicted curves were then tested by experimentally measuring the residual range and counting the blobs of each range segment of two selected stopping particle (primary) tracks which we suspected to be stopping kaon tracks. Then the second degree polynomial computer fit to the plotted data of the measured residual range vs blobs/l00 μm was carried out for each of the two suspected stopping kaon particles. Three points from each curve were picked and superimposed on the theoretical curves. The results were good but showed that it is necessary to measure a sufficiently long residual range, and more than one segment of blob-counts should be used along the measured residual range for accurate identification of the given particle.Ball State UniversityMuncie, IN 47306

Engineering design often requires the optimisation of multiple objectives, and becomes significantly more difficult and time consuming when the response surfaces are multimodal, rather than unimodal. A surrogate model, also known as a metamodel, can be used to replace expensive computer simulations, accelerating single and multi-objective optimisation and the exploration of new design concepts. The main research focus of this work is to investigate the use of a neural network surrogate model to improve optimisation of multimodal surfaces. Several significant contributions derive from evaluating the Cascade Correlation neural network as the basis of a surrogate model. The contributions to the neural network community ultimately outnumber those to the optimisation community. The effects of training this surrogate on multimodal test functions are explored. The Cascade Correlation neural network is shown to map poorly such response surfaces. A hypothesis for this weakness is formulated and tested. A new subdivision technique is created that addresses this problem; however, this new technique requires excessively large datasets upon which to train. The primary conclusion of this work is that Cascade Correlation neural networks form an unreliable basis for a surrogate model, despite successes reported in the literature. A further contribution of this work is the enhancement of an open source optimisation toolkit, achieved by the first integration of a truly multi-objective optimisation algorithm.

The discovery of carbon nanotubes by Iijima in 1991 has created a torrent of new research activities. Research on carbon nanotubes ranges from studying their fundamental properties, such as their electron band structure and plasma frequencies, to developing new applications, such as self-assembled nano-circuits and field emission displays. Robust models are now needed to enable a better understanding of the electronic response of carbon nanotubes. We use time-dependent density functional theory to derive a two-fluid two-dimensional (2D) hydrodynamic model describing the collective response of a multiwalled carbon nanotube with dielectric media embedded inside or surrounding the nanotube. We study plasmon hybridization of the nanotube system in the UV range, the stopping force for ion channelling, the dynamical image potential for fast ions, channelled diclusters and point dipoles, and the energy loss for ions with oblique trajectories. Comparisons are made of results obtained from the 2D hydrodynamic model with those obtained from an extension of the 3D Kitagawa model to cylindrical geometries.

We provide contributions to two classical areas of queueing. The first part of this thesis focuses on finding new conditions for a Markov chain on a general state space to be Harris recurrent, positive Harris recurrent or geometrically ergodic. Most of our results show that establishing each property listed above is equivalent to finding a good enough feasible solution to a particular optimal stopping problem, and they provide a more complete understanding of the role Foster's criterion plays in the theory of Markov chains. The second and third parts of the thesis involve analyzing queues from a transient, or time-dependent perspective. In part two, we are interested in looking at a queueing system from the perspective of a customer that arrives at a fixed time t. Doing this requires us to use tools from Palm theory. From an intuitive standpoint, Palm probabilities provide us with a way of computing probabilities of events, while conditioning on sets of measure zero. Many studies exist in the literature that deal with Palm probabilities for stationary systems, but very few treat the non-stationary case. As an application of our main results, we show that many classical results from queueing (in particular ASTA and Little's law) can be generalized to a time-dependent setting. In part three, we establish a continuity result for what we refer to as jump processes. From a queueing perspective, we basically show that if the primitives and the initial conditions of a sequence of queueing processes converge weakly, then the corresponding queue-length processes converge weakly as well in some sense. Here the notion of convergence used depends on properties of the limiting process, therefore our results generalize classical continuity results that exist in the literature. The way our results can be used to approximate queueing systems is analogous to the way phase-type random variables can be used to approximate other types of random variables.

We propose a dynamic programming (DP) approach for pricing American options over a finite time horizon. We model uncertainty in stock price that follows geometric Brownian motion (GBM) and let interest rate and volatility be fixed. A procedure based on dynamic programming combined with piecewise linear interpolation approximation is developed to price the value of options. And we introduce the free boundary problem into our model. Numerical experiments illustrate the relation between value of option and volatility.