Non-linearities and dynamic interactions between state variables are characteristic of complex social systems and processes. In this thesis, we present a new methodology to model these non-linearities and interactions from the large panel datasets available for some of these systems. We build macro-level statistical models that can verify theoretical predictions, and use polynomial basis functions so that each term in the model represents a specific mechanism. This bridges the existing gap between macro-level theories supported by statistical models and micro-level mechanistic models supported by behavioural evidence. We apply this methodology to two important problems in the social sciences, the demographic transition and the transition to democracy. The demographic transition is an important problem for economists and development scientists. Research has shown that economic growth reduces mortality and fertility rates, which reduction in turn results in faster economic growth. We build a non-linear dynamic model and show how this data-driven model extends existing mechanistic models. We also show policy applications for our models, especially in setting development targets for the Millennium Development Goals or the Sustainable Development Goals. The transition to democracy is an important problem for political scientists and sociologists. Research has shown that economic growth and overall human development transforms socio-cultural values and drives political institutions towards democracy. We model the interactions between the state variables and find that changes in institutional freedoms precedes changes in socio-cultural values. We show applications of our models in studying development traps. This thesis comprises the comprehensive summary and seven papers. Papers I and II describe two similar but complementary methodologies to build non-linear dynamic models from panel datasets. Papers III and IV deal with the demographic transition and policy applications. Papers V and VI describe the transition to democracy and applications. Paper VII describes an application to sustainable development.

Stochastic volatility models have long provided a popular alternative to the Black- Scholes-Merton framework. They provide, in a self-consistent way, an explanation for the presence of implied volatility smiles/skews seen in practice. Incorporating jumps into the stochastic volatility framework gives further freedom to nancial mathematicians to t both the short and long end of the implied volatility surface. We present three stochastic volatility models here - the Heston model, the Bates model and the SVJJ model. The latter two models incorporate jumps in the stock price process and, in the case of the SVJJ model, jumps in the volatility process. We analyse the e ects that the di erent model parameters have on the implied volatility surface as well as the returns distribution. We also present pricing techniques for determining vanilla European option prices under the dynamics of the three models. These include the fast Fourier transform (FFT) framework of Carr and Madan as well as two Monte Carlo pricing methods. Making use of the FFT pricing framework, we present calibration techniques for tting the models to option data. Speci cally, we examine the use of the genetic algorithm, adaptive simulated annealing and a MATLAB optimisation routine for tting the models to option data via a leastsquares calibration routine. We favour the genetic algorithm and make use of it in tting the three models to ALSI and S&P 500 option data. The last section of the dissertation provides hedging techniques for the models via the calculation of option price sensitivities. We nd that a delta, vega and gamma hedging scheme provides the best results for the Heston model. The inclusion of jumps in the stock price and volatility processes, however, worsens the performance of this scheme. MATLAB code for some of the routines implemented is provided in the appendix.

O presente trabalho é uma formulação teórica que permite estudar num modelo estocástico, a influência dos erros de classificação na mensuração da prevalência da esquistossomose mansônica. Os erros de classificação são desagregados e identificados como: falhas de leitura por parte do examinador ou preparo inadequado da lâmina; contingências biológicas que possibilitam o aparecimento de ovos não viáveis e a eliminação de ovos contínua por parte dos indivíduos. É apresentada uma solução geral para o problema, bem como soluções para os casos em que se conhece a distribuição de probabilidades do número de ovos de S.mansoni. Uma solução aproximada e independente da forma e dependente dos dois primeiros momentos da distribuição do número de ovos é sugerida. A influência dos erros de classificação pode quantitativamente ser apreciada, através de um conjunto de tabelas elaboradas com diversos valores dos parâmetros intervenientes no problema. / The present paper is a theoretical approach which will, allow studying the influence - in a stochastic model - of errors in classifying the measurement of the prevalence of Schistosomiasis mansoni. The misclassification errors considered are due to: (A) failure of the examiner in either (1) reading or (2) poor technique. (B) biological contingences which will allow for the appearence of (1) sterile eggs, or (2) discontinuity in the elimination of eggs by the carriers. An exact general solution of the problem is presented, as well as solutions for the particular cases in which the probability distribution of S.mansoni eggs counts in known. An approximate solution is suggested, which is independent from the way in which the number of eggs is distributed, but depends upon the first two moments of the probability distribution of the eggs counts. The influence of misclassification errors can be judged in a quantitative way, by means of a set of tables mande up for the different parametric values of the problem.

A novel stochastic earthquake ground motion model is formulated in association with physically interpretable parameters that are capable of efficiently characterizing the complex evolutionary nature of the phenomenon. A multi-modal, analytical, fully non-stationary spectral version of the Kanai-Tajimi (K-T) model is introduced achieving a realistic description of the evolutionary spectral energy distribution of seismic ground motions. The functional forms describing the temporal evolution of the model parameters can efficiently model highly non-stationary power spectral characteristics. The analysis space, where the analytical forms describing the evolution of the model parameters are established, is the energy domain instead of the typical use of the time domain. This space is used in conjunction with a newly defined energy-associated amplitude modulating function. The Spectral Representation Method supports the simulation of sample ground motions realizations. A predictive stochastic model for simulation of earthquake ground motions is developed, using a user-specified earthquake scenario description as input, and resulting in fully nonstationary ground acceleration time-histories at a site of interest. The previously formed analytical non-stationary K-T ground motion model lies at the core of the developed predictive model. An extensive Californian subset of the NGA-West2 earthquake ground motion database is used to develop and calibrate the predictive stochastic model. Sample observations of the model parameters are obtained by fitting the K-T model to the database records, and their resulting marginal distributions are effectively described by simple probability models. Advanced random-effect regression models are established in the normal probabilistic space, capable of linking the stochastic K-T model parameters with the moment magnitude Mw, closest distance Rrup and average shear-wave velocity VS30 at a Californian site of interest. The included random effects take effectively into account the correlation of ground motions pertaining to the same earthquake event, and the fact that each site is expected to have its own effect on the resulting ground motion. The covariance structure of the normal K-T model parameters is next estimated, allowing finally for the complete mathematical description of the predictive stochastic model for a given earthquake scenario. The entirety of the necessary steps for the simulation of the developed predictive stochastic model is provided, resulting in the generation of any number of fully non-stationary ground acceleration time-series that are statistically consistent with the specified earthquake scenario. In an effort to assess the performance and versatility of the developed predictive stochastic model, a list of simple engineering metrics, associated with the characterization of the earthquake ground motion time-series, is studied, and results from simulated earthquake ground acceleration time-series of the developed predictive model are compared with corresponding predictions of pertinent Ground Motion Prediction Equations (GMPEs) for a variety of earthquake and local-site characteristics. The studied set of ground acceleration time-series features includes the Arias intensity IA, the significant duration T5-95 of the strong ground shaking, and the spectral-based mean period of the earthquake record Tm. The predictive stochastic model is next validated against the state-of-the-art NGA-West2 GMPE models. The statistics of elastic response spectra derived by ensembles of synthetic ground motions are compared with the associated response spectra as predicted by the considered NGA-West2 ground motion prediction equations for a wide spectrum of earthquake scenarios. Finally, earthquake non-linear response-history analyses are conducted for a set of representative single- and multi-degree-of-freedom hysteretic structural systems, comparing the seismically induced inelastic structural demand of the considered systems, when subjected to sets of both real strong ground motion records, and associated simulated ground acceleration time-histories as well. The comparisons are performed in terms of seismic structural demand fragility curves.

In finance, various stochastic models have been used to describe the price movements of financial instruments. After Merton's [38] seminal work, several jump diffusion models for option pricing and risk management have been proposed. In this dissertation, we add alpha-stable Levy motion to the process related to dynamics of log-returns in the Black-Scholes model where the volatility is assumed to be constant. We use the sample characteristic function approach in order to study parameter estimation for discretely observed stochastic differential equations driven by Levy noises. We also discuss the consistency and asymptotic properties of the proposed estimators. Simulation results of the model are also presented to show the validity of the estimators. We then propose a new model where the volatility is not a constant. We consider generalized alpha-stable geometric Levy processes where the stochastic volatility follows the Cox-Ingersoll-Ross (CIR) model in Cox et al. [9]. A number of methods have been proposed for estimating parameters for stable laws. However, a complication arises in estimation of the parameters in our model because of the presence of the unobservable stochastic volatility. To combat this complication we use the sample characteristic function method proposed by Press [48] and the conditional least squares method as mentioned in Overbeck and Ryden [47] to estimate all the parameters. We then discuss the consistency and asymptotic properties of the proposed estimators and establish a Central Limit Theorem. We perform simulations to assess the validity of the estimators. We also present several tables to show the comparison of estimators using different choices of arguments ui's. We conclude that all the estimators converge as expected regardless of the choice of ui's. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2019. / FAU Electronic Theses and Dissertations Collection

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 172-181).

Thesis (Ph. D.)--Chalmers tekniska högskola and Göteborgs universitet, 2006. / Includes bibliographical references (p. 219-224) and index.

Chalmers Univ. of Technology and Göteborg Univ., Diss.--Göteborg, 2006.

This dissertation presents a methodology to simulate the dispersion of water droplets in the air flow typical of an Icing Tunnel. It is based on the understanding the physical parameters that influence the uniformity and the distribution of cloud of droplets in the airflow and to connect them with analytical parameters which may be used to describe the dispersion process. Specifically it investigates the main geometrical and physical parameters contributing to the droplets dispersion at different tunnel operative conditions, finding a consistent numerical approach to reproduce the local droplets dynamic, quantifying the possible limits of commercial CFD methods, pulling out the empirical parameters/constant needing to simulate properly the local conditions and validating the results with calibrated experiment. An overview of the turbulence and multiphase flow theories, considered relevant to the Icing Tunnel environment, is presented as well as basic concepts and terminology of particle dispersion. Taylor’s theory of particle dispersion has been taken as starting point to explain further historical development of discrete phase dispersion. Common methods incorporated in commercial CFD software are explained and relative shortcomings underlined. The local aerodynamic condition within tunnel, which are required to perform the calculation with the Lagrangian particle equation of motions, are generated numerically using different turbulent models and are compared to the historical K-ε model. Verification of the calculation is performed with grid independency studies. Stochastic Separated Flow methods are applied to compute the particle trajectories. The Discrete Random Walk, as described in the literature, has been used to perform particle dispersion analysis. Numerical settings in the code are related to the characteristics of the local turbulent condition such as turbulence intensity and length scales. Cont/d.

Stochastic models of biochemical reaction networks are used for understanding the properties of molecular regulatory circuits in living cells. The state of the cell is defined by the number of copies of each molecular species in the model. The chemical master equation (CME) governs the time evolution of the the probability density function of the often high-dimensional state space. The CME is approximated by a partial differential equation (PDE), the Fokker-Planck equation and solved numerically. Direct solution of the CME rapidly becomes computationally expensive for increasingly complex biological models, since the state space grows exponentially with the number of dimensions. Adaptive numerical methods can be applied in time and space in the PDE framework, and error estimates of the approximate solutions are derived. A method for splitting the CME operator in order to apply the PDE approximation in a subspace of the state space is also developed. The performance is compared to the most widely spread alternative computational method.