The introduction of the thesis consists of four parts: first, we motivate our chosen macroeconomic setting by looking at some real world phenomena. For a better understanding of these phenomena, we argue that the mutual dynamic interactions between flScal policy and financial markets need to be closely examined in a macroeconomic framework. Second, we review different strands of the economic literature in order to show that most of the literature has so far exclusively concentrated either on fmancial market dynamics or on flScal policy issues. We conclude that a more integrated model setting is called for in order to explain the dynamic interactions observed in reality. Third, we discuss at length the economic assumptions underlying our model. This avoids multiple repetition later on. Finally, we outline the structure of the thesis and the objectives we pursue in the different chapters. 1. 1 Motivation Fiscal policy and financial market reactions are increasingly receiving world wide attention. The most recent examples are the Maastricht criteria about flScal control, the South-East Asia financial crisis and the resulting IMF policy stance, the high level of public debt in developed and developing countries and the effect on interest rates and economic growth. In contrast to the still underdeveloped theoretical literature on these dynamic links, finding empirical evidence that supports the existence of these links is not a very hard task.

Contains papers based on talks given at the first AMS-IMS-SIAM Joint Summer Research Conference on Mathematics of Finance held at Snowbird. This book includes such topics as modeling, estimation, optimization, control, and risk assessment and management. It is suitable for students interested in mathematical finance.

Since the groundbreaking research of Harry Markowitz into the application of operations research to the optimization of investment portfolios, finance has been one of the most important areas of application of operations research. The use of hidden Markov models (HMMs) has become one of the hottest areas of research for such applications to finance. This handbook offers systemic applications of different methodologies that have been used for decision making solutions to the financial problems of global markets. As the follow-up to the authors’ Hidden Markov Models in Finance (2007), this offers the latest research developments and applications of HMMs to finance and other related fields. Amongst the fields of quantitative finance and actuarial science that will be covered are: interest rate theory, fixed-income instruments, currency market, annuity and insurance policies with option-embedded features, investment strategies, commodity markets, energy, high-frequency trading, credit risk, numerical algorithms, financial econometrics and operational risk. Hidden Markov Models in Finance: Further Developments and Applications, Volume II presents recent applications and case studies in finance and showcases the formulation of emerging potential applications of new research over the book’s 11 chapters. This will benefit not only researchers in financial modeling, but also others in fields such as engineering, the physical sciences and social sciences. Ultimately the handbook should prove to be a valuable resource to dynamic researchers interested in taking full advantage of the power and versatility of HMMs in accurately and efficiently capturing many of the processes in the financial market.

Random variables. Probability generating functions. Exponential-type distributions and maximum likelihood estimation. Branching process, random walk and ruin problem. Markov chains. Algebraic treatment of finite Markov chains. Renewal processes. Some stochastic models of population growth. A general birth process, an equality and an epidemic model. Birth-death processes and queueing processes. A simple illness-death process - fix-neyman processes. Multiple transition probabilities in the simple illness death process. Multiple transition time in the simple illness death process - an alternating renewal process. The kolmogorov differential equations and finite markov processes. Kolmogorov differential equations and finite markov processes - continuation. A general illness-death process. Migration processes and birth-illness-death processes.

This volume collects papers, based on invited talks given at the IMA workshop in Modeling, Stochastic Control, Optimization, and Related Applications, held at the Institute for Mathematics and Its Applications, University of Minnesota, during May and June, 2018. There were four week-long workshops during the conference. They are (1) stochastic control, computation methods, and applications, (2) queueing theory and networked systems, (3) ecological and biological applications, and (4) finance and economics applications. For broader impacts, researchers from different fields covering both theoretically oriented and application intensive areas were invited to participate in the conference. It brought together researchers from multi-disciplinary communities in applied mathematics, applied probability, engineering, biology, ecology, and networked science, to review, and substantially update most recent progress. As an archive, this volume presents some of the highlights of the workshops, and collect papers covering a broad range of topics.

We apply a hidden Markov model of the term structure to modeling the Brazilian swap rate curve. We examine the model's characteristics and its performance in describing the cross-sectional and time-series dynamics of the term structure. Two regimes are identified, a high level and a high volatility regime and a low level and low volatility regime. Both regimes are persistent and are explained by the level and the slope of the term structure. The model is estimated using a Bayesian MCM algorithm that produces consistent standard errors and a reliable method for testing the differences between the model parameters.