A Penalty Method for the Numerical Solution of Hamilton-Jacobi-Bellman (HJB) Equations in Finance

We present a simple and easy to implement method for the numerical solution of a rather general class of Hamilton-Jacobi-Bellman (HJB) equations. In many cases, the considered problems have only a viscosity solution, to which, fortunately, many intuitive (e.g. finite difference based) discretisations can be shown to converge. However, especially when using fully implicit time stepping schemes with their desirable stability properties, one is still faced with the considerable task of solving the resulting nonlinear discrete system. In this paper, we introduce a penalty method which approximates the nonlinear discrete system to first order in the penalty parameter, and we show that an iterative scheme can be used to solve the penalised discrete problem in finitely many steps. We include a number of examples from mathematical finance for which the described approach yields a rigorous numerical scheme and present numerical results.Comment: 18 Pages, 4 Figures. This updated version has a slightly more detailed introduction. In the current form, the paper will appear in SIAM Journal on Numerical Analysi

Characterization of heat transfer in nutrient materials, part 2

A thermal model is analyzed that takes into account phase changes in the nutrient material. The behavior of fluids in low gravity environments is discussed along with low gravity heat transfer. Thermal contact resistance in the Skylab food heater is analyzed. The original model is modified to include: equivalent conductance due to radiation, radial equivalent conductance, wall equivalent conductance, and equivalent heat capacity. A constant wall-temperature model is presented

{\bf τ\tau-Function Evaluation of Gap Probabilities in Orthogonal and Symplectic Matrix Ensembles}

It has recently been emphasized that all known exact evaluations of gap probabilities for classical unitary matrix ensembles are in fact $\tau$-functions for certain Painlev\'e systems. We show that all exact evaluations of gap probabilities for classical orthogonal matrix ensembles, either known or derivable from the existing literature, are likewise $\tau$-functions for certain Painlev\'e systems. In the case of symplectic matrix ensembles all exact evaluations, either known or derivable from the existing literature, are identified as the mean of two $\tau$-functions, both of which correspond to Hamiltonians satisfying the same differential equation, differing only in the boundary condition. Furthermore the product of these two $\tau$-functions gives the gap probability in the corresponding unitary symmetry case, while one of those $\tau$-functions is the gap probability in the corresponding orthogonal symmetry case.Comment: AMS-Late

Laboratory and field measurements of upwelled radiance and reflectance spectra of suspended James River sediments near Hopewell, Virginia

Spectral reflectance characteristics of suspended Bermuda Hundred and Bailey Bay bottom sediments taken from the Hopewell, Va., area were measured in the laboratory for water mixture total suspended solids concentrations between 4 and 173 parts per million. Field spectral reflectance measurements were made of the James River waters near Bermuda Hundred on two occasions. The results of these tests indicate that both Bermuda Hundred and Bailey Bay suspended sediments produce their strongest reflectance in the green and red regions of the spectrum

Laboratory measurements of radiance and reflectance spectra of dilute secondary-treated sewage sludge

The National Aeronautics and Space Administration (NASA), in cooperation with the Environmental Protection Agency (EPA) and the National Oceanic and Atmospheric Administration (NOAA), conducted a research program to evaluate the feasibility of remotely monitoring ocean dumping of waste products such as acid and sewage sludge. One aspect of the research program involved the measurements of upwelled spectral signatures for sewage-sludge mixtures of different concentrations in an 11600-liter tank. This paper describes the laboratory arrangement and presents radiance and reflectance spectra in the visible and near-infrared ranges for concentrations ranging from 9.7 to 180 ppm of secondary-treated sewage sludge mixed with two types of base water. Results indicate that upwelled radiance varies in a near-linear manner with concentration and that the sludge has a practically flat signal response between 420 and 970 nm. Reflectance spectra were obtained for the sewage-sludge mixtures at all wavelengths and concentrations

Laboratory measurements of radiance and reflectance spectra of dilute primary-treated sewage sludge

The feasibility of remotely monitoring ocean dumping of waste products such as acid and sewage sludge is evaluated. The laboratory arrangement, solar simulator, and test results from three experiments conducted in the laboratory are described. Radiance and reflectance spectra are presented for primary-treated sewage sludge mixed with two types of base water. Results indicate that upwelled reflectance varies in a near-linear manner with concentration and that the sludge has a practically flat signal response between 420 and 970 nm. Well-defined upwelled reflectance spectra were obtained for the sewage-sludge mixtures at all wavelengths and concentrations. The spectral-reflectance values appeared to be influenced by the type of base water, but this influence was small, especially for the mixtures with low concentrations of sewage sludge

A Robust Measure of Tidal Circularization in Coeval Binary Populations: The solar-type spectroscopic Binary Population in The Open Cluster M35

We present a new homogeneous sample of 32 spectroscopic binary orbits in the young (~ 150 Myr) main-sequence open cluster M35. The distribution of orbital eccentricity vs. orbital period (e-log(P)) displays a distinct transition from eccentric to circular orbits at an orbital period of ~ 10 days. The transition is due to tidal circularization of the closest binaries. The population of binary orbits in M35 provide a significantly improved constraint on the rate of tidal circularization at an age of 150 Myr. We propose a new and more robust diagnostic of the degree of tidal circularization in a binary population based on a functional fit to the e-log(P) distribution. We call this new measure the tidal circularization period. The tidal circularization period of a binary population represents the orbital period at which a binary orbit with the most frequent initial orbital eccentricity circularizes (defined as e = 0.01) at the age of the population. We determine the tidal circularizationperiod for M35 as well as for 7 additional binary populations spanning ages from the pre main-sequence (~ 3 Myr) to late main-sequence (~ 10 Gyr), and use Monte Carlo error analysis to determine the uncertainties on the derived circularization periods. We conclude that current theories of tidal circularization cannot account for the distribution of tidal circularization periods with population age.Comment: 37 pages, 9 figures, to be published in The Astrophysical Journal, February 200