Teaching an Old Dog New Tricks: Improved Estimation of the Parameters of Stochastic Differential Equations by Numerical Solution of the Fokker-Planck Equation

Many stochastic differential equations (SDEs) do not have readily available closed-form expressions for their transitional probability density functions (PDFs). As a result, a large number of competing estimation approaches have been proposed in order to obtain maximum-likelihood estimates of their parameters. Arguably the most straightforward of these is one in which the required estimates of the transitional PDF are obtained by numerical solution of the Fokker-Planck(or forward-Kolmogorov) partial differential equation. Despite the fact that this method produces accurate estimates and is completely generic, it has not proved popular in the applied literature. Perhaps this is attributable to the fact that this approach requires repeated solution of a parabolic partial differential equation to obtain the transitional PDF and is therefore computationally quite expensive. In this paper, three avenues for improving the reliability and speed of this estimation method are introduced and explored in the context of estimating the parameters of the popular Cox-Ingersoll-Ross and Ornstein-Uhlenbeck models. The recommended algorithm that emerges from this investigation is seen to offer substantial gains in reliability and computational time.stochastic di®erential equations, maximum likelihood, ¯nite di®erence, ¯nite element, cumulative

Estimating the Payoffs of Temperature-based Weather Derivatives

Temperature-based weather derivatives are written on an index which is normally defined to be a nonlinear function of average daily temperatures. Recent empirical work has demonstrated the usefulness of simple time-series models of temperature for estimating the payoffs to these instruments. This paper argues that a more direct and parsimonious approach is to model the time-series behaviour of the index itself, provided a sufficiently rich supply of historical data is available. A data set comprising average daily temperature spanning over a hundred years for four Australian cities is assembled. The data is then used to compare the actual payoffs of temperature-based European call options with the expected payoffs computed from historical temperature records and two time-series approaches. It is concluded that expected payoffs computed directly from historical records perform poorly by comparison with the expected payoffs generated by means of competing time-series models. It is also found that modeling the relevant temperature index directly is superior to modeling average daily temperatures.Temperature, Weather Derivatives, Cooling Degree Days, Time-series Models.

The Devil is in the Detail: Hints for Practical Optimisation

Finding the minimum of an objective function, such as a least squares or negative log-likelihood function, with respect to the unknown model parameters is a problem often encountered in econometrics. Consequently, students of econometrics and applied econometricians are usually well-grounded in the broad differences between the numerical procedures employed to solve these problems. Often, however, relatively little time is given to understanding the practical subtleties of implementing these schemes when faced with illbehaved problems. This paper addresses some of the details involved in practical optimisation, such as dealing with constraints on the parameters, specifying starting values, termination criteria and analytical gradients, and illustrates some of the general ideas with several instructive examples.gradient algorithms, unconstrained optimisation, generalised method of moments.

Design data for brazed Rene 41 honeycomb sandwich

Strength data, creep data and residual strength data after cyclic thermal exposure were obtained at temperatures from 78 K to 1144 K (-320 F to 1600 F). The influences of face thickness, core depth, core gage, cell size and thermal/stress exposure conditions on the mechanical design properties were investigated. A braze alloy and process was developed that is adequate to fully develop the strength of the honeycomb core while simultaneously solution treating and aging the Rene 41 fact sheets. New test procedures and test specimen configurations were developed to avoid excessive thermal stresses during cyclic thermal exposure

From the Technical to the Personal: Teaching and Learning Health Insurance Regulation and Reform

In the Fall of 2016, I taught Health Law and Policy for the fourth consecutive semester. Over time, one thing has become increasingly clear: the aspect of this course that I work with most closely as a scholar—the regulation of health care financing and insurance, including the Patient Protection and Affordable Care Act (ACA)—is also the material that I find the most challenging to teach. Every time I reflect on teaching this material, and hear from students about how they learn this material, the thing that stands out is how critical it is that my students understand the profound impact that this technical subject has on individuals’ lives. Health insurance regulation simultaneously shapes and is an expression of social values. It defines the types of harms we expect individuals to shoulder on their own and what we are willing to mitigate collectively, as a society. Every rule that expands the scope of insurance—whether private or social insurance—is a signal of greater social solidarity with respect to each other’s health. Every contraction of the scope of insurance is the opposite, and leaves individuals more vulnerable to poor health or financial insecurity due to high health care spending. These broader implications are what draw me to the topic—as a teacher and as a scholar. My ultimate goal is for my students to understand this social meaning: why insurance is regulated as it is, how that regulation reflects larger social values, and the impact—both intended and unintended—that insurance regulation has on the shape of our society. When asked to write this Article on teaching health insurance regulation and reform for the Saint Louis University Law Journal Teaching Issue, I took the opportunity to confirm that what I thought worked in the classroom was actually working. To this end, I asked two of my former students to reflect, as my co-authors, on learning health insurance regulation and reform in my Health Law and Policy class, and I discovered that some of my aims were hitting the mark and others could benefit from refinement. In Part I of this Article, I describe my goals and approaches in teaching these topics as well as why this material can be difficult to teach. My student co-authors reflect on their own experiences in learning this material in Part II, including what they took away from it and what questions remain. In the final Part of the Article, I highlight how my co-authors’ insights have informed my teaching

Guidelines for the management of degenerative cervical myelopathy and spinal cord injury: an introduction to a focus issue

Study Design: Introduction to a guidelines project. Objectives: The objective of this focus issue is to present guidelines that outline how to best manage patients with degenerative cervical myelopathy (DCM) and spinal cord injury (SCI). Topics addressed in this focus issue include: 1) management strategies for patients with mild, moderate and severe DCM; and 2a) timing of surgical decompression; b) the use of methylprednisolone sodium succinate; c) the type and timing of anticoagulation strategies; d) the role of magnetic resonance imaging in clinical decision making and outcome prediction; and e) the type and timing of rehabilitation in patients with SCI. Methods: Systematic reviews were conducted to address key clinical questions and to synthesize the current body of evidence. A multidisciplinary guideline development group used the results of these reviews, along with their clinical expertise, to develop clinical practice guidelines, in a process that adhered to methodology proposed by the Grades of Recommendation, Assessment, Development and Evaluation (GRADE) Working Group. Results: The multidisciplinary guideline development group combined the systematic review findings with their clinical expertise and opinions to formulate recommendations on how to manage patients with DCM and SCI. Conclusions: These guidelines will serve as tools to assist clinicians in their decision making by offering a perspective that combines the available evidence, expertise from a variety of clinicians, and patient values

Life interrupted and life regained? Coping with stroke at a young age

Stroke is a leading cause of disability across the developed world, affecting an increasing number of younger people. In this article, we seek to understand the experience of stroke as a disabling life situation among young people and the strategies that they use to recover and cope. Directed content analysis was conducted from interviews with 17 community-dwelling stroke survivors aged 55 years and younger across the United Kingdom. The sample was drawn from a larger maximum variation sample of stroke survivors. Using the sociological concepts of biographical disruption and biographical repair as a guide, excerpts from the interviews pertaining to aspects of the patients’ life that were interrupted, in addition to how they coped with the changes, were selected and analysed. All individuals described an ‘‘altered sense of self,’’ a theme that included loss of identity, family disruption, and/or loss of valued activities. Individuals sought to adapt their sense of self by seeking external support, by restoring normality, and/or through positive reflection. Despite the adapted self that emerged, most individuals continued to experience impairments. While young stroke survivors adapt to their illness over time, they continue to experience impairments and disruptions in their personal and work lives.Aholistic model of rehabilitation that helps individuals regain the capacity for everyday activities related to work, family life, and leisure can begin to address the emotional ramifications of diseases such as stroke, restore wellness, and work towards minimizing the burden felt by family caregivers and children