Controllable Non-Markovianity for a Spin Qubit in Diamond

We present a flexible scheme to realize non-artificial non-Markovian dynamics of an electronic spin qubit, using a nitrogen-vacancy center in diamond where the inherent nitrogen spin serves as a regulator of the dynamics. By changing the population of the nitrogen spin, we show that we can smoothly tune the non-Markovianity of the electron spin's dynamic. Furthermore, we examine the decoherence dynamics induced by the spin bath to exclude other sources of non-Markovianity. The amount of collected measurement data is kept at a minimum by employing Bayesian data analysis. This allows for a precise quantification of the parameters involved in the description of the dynamics and a prediction of so far unobserved data points.Comment: 12 pages, 9 figure, including supplemental materia

Multi-Period Credit Default Prediction - A Survival Analysis Approach

The book deals with the problem to estimate credit default probabilities under a flexible multi-period prediction horizon. Multi-period predictions are naturally desirable because the maturity of loans usually spans several periods. However, single-period models largely prevail in the literature so far due to their simplicity. Predicting over multiple periods indeed entails certain challenges that do not arise within a single-period view. Among the main contributions of this work to the literature is to show that there are relatively simple solutions to these challenges available. From a methodological point of view, a survival analysis approach is used. In a survival analysis context, the time until default (or lifetime) is the central variable under investigation as opposed to the traditional approach of reducing the information to a binary variable representing the default event. Modeling the time until default has the advantage that both the timing of default events and censored data are utilized. Since both issues gain importance as the prediction horizon grows it is no coincidence that a survival analysis approach is selected for the multi-period prediction problem. The main results of the work are the following. First, a new index for measuring the predictive accuracy of default predictions is proposed and its advantages over commonly used indices are shown both theoretically and by an empirical analysis. This is part of the second chapter which further includes new methods of statistical inference for the new index. In the third chapter, default prediction models for the case of panel datasets with time-varying covariates are dealt with. A new approach is developed that is simpler than the models available in the literature so far. In an empirical study concerning North American public firms, we provide evidence that the proposed approach delivers more accurate predictions than its competitors as well. In the final chapter, the problem of assigning default probability estimates to given rating grades is examined. If default events are rare, standard approaches have certain drawbacks. As an alternative, an empirical Bayes approach is presented that mitigates the effects of data sparseness. The new estimator is applied to a comprehensive sample of sovereign bonds. Among the main findings of the empirical part is that capital requirements for sovereign bonds are likely to be underestimated by using standard approaches but not when using the empirical Bayes estimator

Application of Absorbing Markov Chains to the Assessment of Education Attainment Rates within Air Force Materiel Command Civilian Personnel

Increasing the education levels of an organization is a common response when attempting to improve organizational performance; however, organizational performance improvements are seldom found when the current and future workforce education levels are unknown. In this research, absorbing Markov chains are used to probabilistically forecast the educational composition of the Air Force Materiel Command civilian workforce to enable organizational performance improvements. Through the purposeful decoupling of effects resulting from recent workforce arrivals and education level progressions, this research attempts to determine the implications that stationarity assumptions have throughout the model development process of an absorbing Markov chain. The results of the analysis indicate that the four combinations of stationarity assumptions perform similarly at representing the historical data and that the forecasted educational attainment rates of the Air Force Materiel Command civilian workforce are expected to increase significantly

Credit Rating Dynamics and Markov Mixture Models

Despite overwhelming evidence to the contrary, credit migration matrices, used in many credit risk and pricing applications, are typically assumed to be generated by a simple Markov process. In this paper we propose a parsimonious model that is a mixture of (two) Markov chains. We estimate this model using credit rating histories and show that the mixture model statistically dominates the simple Markov model and that the differences between two models can be economically meaningful. The non-Markov property of our model implies that the future distribution of a firm's ratings depends not only on its current rating but also on its past rating history. Indeed we find that two firms with identical credit ratings can have substantially different transition probability vectors