Brown University Center for Statistical Sciences Seminar
Research Scientist, Regenstrief Institute for Health Care, Indiana University School of Medicine and Department of Biostatistics Harvard School of Public Health, Indianapolis, IN | |
*Reception Following Seminar at 167 Angell Street, 2nd Floor Conference Room |
Abstract: There has been increasing emphasis on cost comparison and cost-effectiveness analysis in health care delivery systems. However, correct analysis of health care costs may be impeded by several characteristics of health care costs, including (1) a high proportion of patients who have zero observations and (2) a highly skewed distribution for non-zero observations. Motivated by this type of data, some new statistical methods will be discussed that can handle these types of problems. These methods will be illustrated using some real data sets.
Stochastic Systems Seminar
Abstract: Although Brownian motion and normal distribution have been widely used in finance, two puzzles have got much attention recently; namely the leptokurtic feature that empirically the return distribution of assets may have a higher peak and two (asymmetric) heavier tails than those of the normal distribution, and an empirical abnormality called "volatility smile" in option pricing. To incorporate these, the double exponential jump diffusion model was proposed before, in which the price of the underlying asset is modeled by two parts, a continuous part driven by Brownian motion, and a jump part with the jump size having a double exponential distribution.
The current paper shows that, in addition to the leptokurtic feature and "volatility smile", the model is simple enough to produce analytical solutions for a variety of option pricing problems, including barrier and perpetual American options, in terms of the Laplace transform and the $Hh$ function. The numerical implementation will also be discussed. As a by produce, this also gives a closed form solution for the first passage time of the jump diffusion processes, which might be of independent interest in applied probability.
Brown University, Chemistry Department,
Special Interdisciplinary Lecture Series on the Simulation
and Visualization of Physical Phenomena
Host: Professor Jimmie Doll, Brown University, Department of Chemistry |
Brown Analysis Seminar
Scientific Computing Seminar
Abstract: Consider a piecewise smooth function for which the pseudo-spectral coefficients are given. It is well known that while spectral partial sums yield exponentially convergent approximations for smooth functions, the results for piecewise smooth functions are poor, with spurious oscillations developing near the discontinuities and a much reduced overall convergence rate. This behavior, known as the Gibbs phenomenon, is considered as one of the major drawbacks in the application of spectral methods. Various types of reconstruction methods for the recovery of piecewise smooth functions have met with varying degrees of success. The Gegenbauer reconstruction method, originally proposed by Gottlieb et. al. has the particularly impressive ability to reconstruct piecewise analytic functions with exponential convergence up to the points of discontinuity. However, it has been sharply criticized for its high cost and susceptibility to round-off error. Here, a new approach to Gegenbauer reconstruction is considered resulting in a reconstruction method that is less computationally intensive and costly, yet still enjoys superior convergence. The idea is to create a procedure that combines the well known exponential filtering method in smooth regions away from the discontinuities with the Gegenbauer reconstruction method in regions close to the discontinuities. This hybrid approach benefits from both the simplicity of exponential filtering and the high resolution properties of the Gegenbauer reconstruction method. Several examples are discussed.
Department of Mathematics Colloquium
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