A stochastic programming model for funding single premium deferred annuities

Single Premium Deferred Annuities (SPDAs) are investment vehicles, offered to investors by insurance companies as a means of providing income past their retirement age. They are mirror images of insurance policies. However, the propensity of individuals to shift part, or all, of their investment into different annuities creates substantial uncertainties for the insurance company. In this paper we develop amultiperiod, dynamic stochastic program that deals with the problem of funding SPDA liabilities. The model recognizes explicitly the uncertainties inherent in this problem due to both interest rate volatility and the behavior of individual investors. Empirical results are presented with the use of the model for the funding of an SPDA liability stream using government bonds, mortgage-backed securities and derivative products. Research partially supported by NSF grants CCR-9104042 and SES-91-00216, and AFOSR grant 91-0168. Computing resources were made available by AHPCRC at the University of Minnesota, by NPAC at Syracuse University, New York, and by the GRASP Laboratory at Computer Science Department at University of Pennsylvania.     

Reversible 1,1‐Hydroboration: Boryl Insertion into a CN Bond and Competitive Elimination of HBR2 or RH

Boranes with the general formula of HBR₂ have been found to undergo a facile 1,1‐hydroboration reaction with pyrido[1,2‐a]isoindole ( A ), resulting in insertion of a BR₂ unit into a C? N bond and the formation of a variety of BN heterocycles. Investigation on the thermal reactivity of the BN heterocycles revealed that these molecules have two distinct and competitive thermal elimination pathways: HBR₂ elimination (or retro‐hydroboration) versus R? H elimination, depending on the R group on the B atom and the chelate backbone. Mechanistic aspects of these highly unusual reactions have been established from both experimental and computational evidence. Adduct formation between HBR₂ and A was found to be the key intermediate in 1,1‐hydroboration of A .     

Donor‐Appended N,C‐Chelate Organoboron Compounds: Influence of Donor Strength on Photochromic Behaviour

Recently, four‐coordinated N,C‐chelate organoboron compounds have been found to show many interesting photochemical transformations depending on the nature of their chelating framework. As such, the effect of substitution on the chelate ligand has been well‐established and understood, but the impact of the aryl groups attached to the boron atom remains less clear. To investigate the effect of enhanced charge‐transfer character, a series of new N,C‐chelate organoboron compounds with donor‐functionalized aryl groups have been synthesized and characterized using NMR, UV/Vis, and electrochemical methods. These compounds were found to possess bright and tunable charge‐transfer luminescence which is dependent on the donor strength of the amino substituent. In addition, some of these compounds undergo photochromic switching, producing dark isomers of various colors. This work establishes that donor‐functionalization of the aryl groups in N,C‐chelate boron compounds is an effective strategy for tuning both the photophysical and photochemical properties of such systems. The new findings also help elucidate the influence of electronic structure on the photoreactivity of N,C‐chelate organoboron compounds which appears to be as important as steric crowding around the boron atom.     

Branching random walks II

A general method is developed with which various theorems on the mean square convergence of functionals of branching random walks are proven. The results cover extensions and generalizations of classical central limit analogues as well as a result of a different type.     

Microcrystallography, high-pressure cryocooling and BioSAXS at MacCHESS

The Macromolecular Diffraction Facility at the Cornell High Energy Synchrotron Source (MacCHESS) is a national research resource supported by the National Center for Research Resources of the US National Institutes of Health. MacCHESS is pursuing several research initiatives designed to benefit both CHESS users and the wider structural biology community. Three initiatives are presented in further detail: microcrystallography, which aims to improve the collection of diffraction data from crystals a few micrometers across, or small well diffracting regions of inhomogeneous crystals, so as to obtain high-resolution structures; pressure cryocooling, which can stabilize transient structures and reduce lattice damage during the cooling process; and BioSAXS (small-angle X-ray scattering on biological solutions), which can extract molecular shape and other structural information from macromolecules in solution.     

A hierarchical location-allocation model with travel based on expected referral distances

The hierarchical p-median location-allocation model assumes that patrons always travel to the closest facility of appropriate level and that their interests are best served when the distances they must travel to do this are minimized. This assumption about travel behavior is unrealistic, patrons in the real world are known, for instance, to bypass lower level facilities that can serve their needs to attend higher level facilities. We introduce the concept of “expected distance under referral” to deal with such irrationality and incorporate it into a location-allocation model that minimizes the negative effects of such irrational behavior. We demonstrate the model with several types of non-optimal travel behavior.     

Level discrimination as a function of level for tones from 0.25 to 16 kHz

Difference limens for level (delta L in dB = 20 log [(p + delta p)/p], where p is pressure) were measured as a function of level for tones at 0.25, 0.5, 1, 2, 4, 8, 10, 12, 14, and 16 kHz. At each frequency, test levels encompassed the range from near threshold to 95 dB SPL in steps of 10 dB or smaller. The stimulus duration was 500 ms and the interstimulus interval was 250 ms. An adaptive two-alternative forced-choice procedure with feedback was used. Results for six normal listeners show individual differences among listeners, but the general trends seen in the average data clearly are present in the individual data and show the following. First, the delta Ls at all but the highest frequencies are generally smaller at high levels than at low levels. Second, the delta Ls at equal SPLs are largely independent of frequency up to about 4 kHz, but increase with frequency above 4 kHz. Third, at 8 and 10 kHz, the delta Ls are clearly nonmonotonic functions of level, showing consistent deterioration in the mid-level delta Ls relative to the low- and high-level delta Ls. The present data are discussed qualitatively in terms of current models of level discrimination.     

Perceptual weights in auditory level discrimination

Perceptual weights in level discrimination (also called intensity discrimination) were determined for 3-, 7-, 15-, and 24-component tone complexes with flat spectral envelopes using a correlational paradigm. Each frequency component was randomly and independently perturbed in level oneach presentation. For the target interval, frequency-component levels were additionally increased by the level increment to be detected, deltaL [= 201og10((p + deltap)/p), where p is pressure]. Weights were calculated from the across-trial correlation between the level perturbations for each frequency component and the interval chosen by the listener. Two conditions were investigated: (1) deltaL was equal across frequency components, and (2) deltaL increased progressively across frequency components. For both conditions, data for four listeners usually showed the greatest weight for the highest frequency component. The two-to-four highest frequency components generally were most important for level discrimination. The effect of increasing deltaL progressively with frequency was small and inconsistent. Additional measurements showed that flanking noise maskers designed to mask spread of excitation caused only small and generally unsystematic changes to the weights. Overall, these results indicate that listeners combine information across a wide range of auditory channels to arrive at a decision for level discrimination, but the weighting of channels appears to be suboptimal.