Stochastic continuous-time cash flows: A coupled linear-quadratic model

<p>The focal point of this dissertation is stochastic continuous-time cash flow models. These models, as underpinned by the results of this study, prove to be useful to describe the rich and diverse nature of trends and fluctuations in cash flow randomness. Firstly, this study considers an important preliminary question: can cash flows be fully described in continuous time? Theoretical and empirical evidence (e.g. testing for jumps) show that under some not too stringent regularities, operating cash flow processes can be well approximated by a diffusion equation, whilst investing processes -preferably- will first need to be rescaled by a system-size variable. Validated by this finding and supported by a multitude of theoretical considerations and statistical tests, the main conclusion of this dissertation is that an equation consisting of a linear drift function and a complete quadratic diffusion function (hereafter: “the linear-quadratic model”) is a specification preferred to other specifications frequently found in the literature. These so-called benchmark processes are: the geometric and arithmetic Brownian motions, the mean-reverting Vasicek and Cox, Ingersoll and Ross processes, and the modified Square Root process. Those specifications can all be considered particular cases of the generic linear-quadratic model. The linear-quadratic model is classified as a hybrid model since it is shown to be constructed from the combination of geometric and arithmetic Brownian motions. The linear-quadratic specification is described by a fundamental model, rooted in well-studied and generally accepted business and financial assumptions, consisting of two coupled, recursive relationships between operating and investing cash flows. The fundamental model explains the positive feedback mechanism assumed to exist between the two types of cash flows. In a stochastic environment, it is demonstrated that the linear-quadratic model can be derived from the principles of the fundamental model. There is no (known) general closed-form solution to the hybrid linear-quadratic cash flow specification. Nevertheless, three particular and three approximated exact solutions are derived under not too stringent parameter restrictions and cash flow domain limitations. Weak solutions are described by (forward or backward) Fokker-Planck- Kolmogorov equations. This study shows that since the process is converging in time (that is, approximating a stable probability distribution), (uncoupled) investing cash flows can be described by a Pearson diffusion process approaching a stationary Person-IV probability density function, more appropriately a Student diffusion process. In contrast, (uncoupled) operating cash flow processes are diverging in time, that is exploding with no stable probability density function, a dynamic analysis in a bounded cash flow domain is required. A suggested solution method normalises a general hypergeometric differential equation, after separation of variables, which is then transformed into a Sturm-Liouville specification, followed by a choice of three separate second transformations. These second transformations are the Jacobi, the Hermitian and the Schrödinger, each yielding a homonymous equation. Only the Jacobi transformation provides an exact solution, the other two transformations lead to approximated closed-form general solutions. It turns out that a space-time density function of operating cash flow processes can be construed as the multiplication of two (independent) time-variant probability distributions: a stationary family of distributions akin to Pearson’s case 2, and the evolution of a standard normal distribution. The fundamental model and the linear-quadratic specification are empirically validated by three different statistical tests. The first test provides evidence that the fundamental model is statistically significant. Parameter values support the conclusion that operating and investing processes are converging to overall long-term stable values, albeit with significant stochastic variation of individual firms around averages. The second test pertains to direct estimation from approximated SDE solutions. Parameter values found, are not only plausible but agree with theoretical considerations and empirical observations elaborated in this study. The third test relates to an approximated density function and its associated approximated maximum likelihood estimator. The Ait-Sahalia- method, in this study adapted to derive the Fourier coefficients (of the Hermite expansion) from a (closed) system of moment ODEs, is considered a superior technique to derive an approximated density function associated with the linear-quadratic model. The maximum likelihood technique employed, proper for high-parametrised estimations, includes re-parametrisation (based on the extended invariance principle) and stepwise maximisation. Reported estimation results support the hypothesised superiority of the linear-quadratic cash flow model, either in complete (five-parameter form) or in a reduced-parameter form, in comparison to the examined five benchmark processes.</p>

Stochastic continuous-time cash flows: A coupled linear-quadratic model

<p>The focal point of this dissertation is stochastic continuous-time cash flow models. These models, as underpinned by the results of this study, prove to be useful to describe the rich and diverse nature of trends and fluctuations in cash flow randomness. Firstly, this study considers an important preliminary question: can cash flows be fully described in continuous time? Theoretical and empirical evidence (e.g. testing for jumps) show that under some not too stringent regularities, operating cash flow processes can be well approximated by a diffusion equation, whilst investing processes -preferably- will first need to be rescaled by a system-size variable. Validated by this finding and supported by a multitude of theoretical considerations and statistical tests, the main conclusion of this dissertation is that an equation consisting of a linear drift function and a complete quadratic diffusion function (hereafter: “the linear-quadratic model”) is a specification preferred to other specifications frequently found in the literature. These so-called benchmark processes are: the geometric and arithmetic Brownian motions, the mean-reverting Vasicek and Cox, Ingersoll and Ross processes, and the modified Square Root process. Those specifications can all be considered particular cases of the generic linear-quadratic model. The linear-quadratic model is classified as a hybrid model since it is shown to be constructed from the combination of geometric and arithmetic Brownian motions. The linear-quadratic specification is described by a fundamental model, rooted in well-studied and generally accepted business and financial assumptions, consisting of two coupled, recursive relationships between operating and investing cash flows. The fundamental model explains the positive feedback mechanism assumed to exist between the two types of cash flows. In a stochastic environment, it is demonstrated that the linear-quadratic model can be derived from the principles of the fundamental model. There is no (known) general closed-form solution to the hybrid linear-quadratic cash flow specification. Nevertheless, three particular and three approximated exact solutions are derived under not too stringent parameter restrictions and cash flow domain limitations. Weak solutions are described by (forward or backward) Fokker-Planck- Kolmogorov equations. This study shows that since the process is converging in time (that is, approximating a stable probability distribution), (uncoupled) investing cash flows can be described by a Pearson diffusion process approaching a stationary Person-IV probability density function, more appropriately a Student diffusion process. In contrast, (uncoupled) operating cash flow processes are diverging in time, that is exploding with no stable probability density function, a dynamic analysis in a bounded cash flow domain is required. A suggested solution method normalises a general hypergeometric differential equation, after separation of variables, which is then transformed into a Sturm-Liouville specification, followed by a choice of three separate second transformations. These second transformations are the Jacobi, the Hermitian and the Schrödinger, each yielding a homonymous equation. Only the Jacobi transformation provides an exact solution, the other two transformations lead to approximated closed-form general solutions. It turns out that a space-time density function of operating cash flow processes can be construed as the multiplication of two (independent) time-variant probability distributions: a stationary family of distributions akin to Pearson’s case 2, and the evolution of a standard normal distribution. The fundamental model and the linear-quadratic specification are empirically validated by three different statistical tests. The first test provides evidence that the fundamental model is statistically significant. Parameter values support the conclusion that operating and investing processes are converging to overall long-term stable values, albeit with significant stochastic variation of individual firms around averages. The second test pertains to direct estimation from approximated SDE solutions. Parameter values found, are not only plausible but agree with theoretical considerations and empirical observations elaborated in this study. The third test relates to an approximated density function and its associated approximated maximum likelihood estimator. The Ait-Sahalia- method, in this study adapted to derive the Fourier coefficients (of the Hermite expansion) from a (closed) system of moment ODEs, is considered a superior technique to derive an approximated density function associated with the linear-quadratic model. The maximum likelihood technique employed, proper for high-parametrised estimations, includes re-parametrisation (based on the extended invariance principle) and stepwise maximisation. Reported estimation results support the hypothesised superiority of the linear-quadratic cash flow model, either in complete (five-parameter form) or in a reduced-parameter form, in comparison to the examined five benchmark processes.</p>

A preliminary exploration of the micro-scale behaviour of capillary barrier effect using microfluidics

Capillary barrier effect (CBE) is employed in a large number of geotechnical applications to decrease deep percolation or increase slope stability. However, the micro-scale behaviour of CBE is rarely investigated, and thus hampers the scientific design of capillary barrier systems. This study uses microfluidics to explore the micro-scale behaviour of CBE. Capillarity-driven water flow processes from fine to coarse porous media with different pore topologies and sizes were performed and analysed. The experimental results demonstrate that the basic physics of CBE is the preferential water movement into the fine porous media due to the larger capillarity. The effects of CBE on water flow processes can be identified as delaying the occurrence of breakthrough into the coarse porous media and increasing the water storage of the fine porous media. The CBE can impede the increase of the normalized length and decrease the normalized width of the water front, suggesting that the two normalized parameters are potential indicators to assess the performance of CBE at micro scale. CBE can be formed in square and honeycomb networks with the ratio of coarse to fine pore throat width larger than 2.0 when gravity is neglected, and its performance can be affected by pore topology and size.

Rapid multigram scale end-to-end continuous flow synthesis of sulfonylurea anti-diabetes drugs: Gliclazide, chlorpropamide and tolbutamide

Herein we report multigram scale robust, efficient, and safe end-to-end continuous flow processes for the diabetes sulfonylurea drugs gliclazide, chlorpropamide and tolbutamide. The drugs were prepared via the treatment of an amine with a haloformate affording carbamate which was subsequently treated with a sulfonamide to afford sulfonylurea. Gliclazide was afforded in 87 % yield within 2.5 min total residence time with 26 g/h throughput; 0.2 Kg of the drug was produced in 8 h of running the system continuously. Chlorpropamide and tolbutamide were both afforded in 94 % yield within 1 min residence time with 184-188 g/h throughput; 1.4-1.5 Kg of the drugs was produced in 8 h of running the system continuously. N-substituted carbamates were used as safe alternatives to the hazardous isocyanates in constructing the sulfonyl urea moiety.

Exploring Reservoir within Hugin Formation in Theta Vest Structure using 4-D Seismic and Machine Learning Approach

This paper aims to identify the oil distribution using 4-D seismic below a complex 3-D surface in Hugin Formation using machine learning and geobody detection. The exploration well 15/9-19-SR, drilled to the Theta Vest structure, was based on the interpretation of reprocessed ST8215R 3-D seismic survey data from 1991 in the Sleipner area, encountered oil in the Jurassic Hugin Formation. The drills stem test showed outstanding production capacities through time, with low water cut and low GOR. 4-D seismic has all the traditional benefits of 3-D seismic. A significant additional potential benefit is that fluid-flow processes can be directly imaged. The 4-D seismic analysis was conducted in 2012 to repeat the 3-D seismic surveys and analyze images in time-lapse mode to monitor time-varying fluid-flow processes during reservoir production. A comprehensive study of the structure and the discovery has been performed and is reported. The DNN method to predict facies far away from existing production wells by using facies log well to supervise seismic inversion created by the Seismic Color Inversion method. It can detect some oil pockets distribution and risk the well planning and the right candidate for new proposed wells.