An equivalence result for VC classes of sets

Let R and θ be infinite sets and let A # R × θ. We show that the class of projections of A onto R is a Vapnik–Chervonenkis (VC) class of sets if and only if the class of projections of A onto θ is a VC class. We illustrate the result in the context of semiparametric estimation of a transformation model. In this application, the VC property is hard to establish for the projection class of interest but easy to establish for the other projection class

Do Options Contain Information About Excess Bond Returns?

There is strong empirical evidence that risk premia in long-term interest rates are time-varying. These risk premia critically depend on interest rate volatility, yet existing research has not examined the impact of time-varying volatility on excess returns for long-term bonds. To address this issue, we incorporate interest rate option prices, which are very sensitive to interest rate volatility, into a dynamic model for the term structure of interest rates. We estimate three-factor affine term structure models using both swap rates and interest rate cap prices. When we incorporate option prices, the model better captures interest rate volatility and is better able to predict excess returns for long-term swaps over short-term swaps, both in- and out-of-sample. Our results indicate that interest rate options contain valuable information about risk premia and interest rate dynamics that cannot be extracted from interest rates alone.

The thermal and mechanical behavior of poly(ethylene terephthalate) fibers incorporating novel thermotropic liquid crystalline polymers/

This dissertation explores the potential of improving the performance of poly(ethylene terephthalate) fibers by incorporating novel thermotropic liquid crystalline polymers. To determine if a system exhibited desirable characteristics, a screening procedure was developed to assess the various blends. Evaluations focused on blend compositions ranging from 2 to 20 wt.% LCP. Fibers were obtained by melt extrusion and the effect of processing conditions, i.e. spinning temperature, stretch ratio, and post treatment evaluated. The fibers were tested for mechanical performance, dimensional instability (shrinkage), and the development of shrinkage stresses. Test results were used to determine the critical parameters necessary for in-situ reinforcement and to develop strategies for improving LCP architecture and processing techniques. The novel TLCP\u27s incorporated into the PET were mesogenic copolymers containing either alternating or random flexible groups within the polymer backbone. The flexible moieties were used to promote compatibility between the PET matrix phase and the TLCPs. Two systems were found to significantly improve fiber stiffness compared to neat PET fibers. A Random Copolymer based on the reaction of oxyethylene substituted hydroquinone, ethylene glycol, and terephthaloyl chloride was found to effectively enhance the performance of PET fibers. Fibers containing only 5% TLCP exhibited a 50% increase in modulus, while maintaining an ultimate strength equivalent to the PET control. The thermal behavior of the 5% blend, as determined by free shrinkage and force-temperature experiments, was similar to the PET control. A segmented block copolymer consisting of rigid-rod, diad, and flexible coil segments was also found to improve the performance of PET fibers. At a concentration of 20 wt. percent, the alternating block copolymer, Triad2 (2:6:7), increased the tensile modulus of the fibers 40% and decreased free shrinkage by 20% compared to neat PET. The mechanism of reinforcement for these systems is unclear, but morphological, thermal and mechanical evidence suggest that the TLCPs are modifying the PET matrix and not providing true mechanical reinforcement

AN EQUIVALENCE RESULT FOR VC CLASSES OF SETS

Let R and Q be infinite sets and let A ʕ R ϫ Q+ We show that the class of projections of A onto R is a Vapnik-Chervonenkis~VC! class of sets if and only if the class of projections of A onto Q is a VC class+ We illustrate the result in the context of semiparametric estimation of a transformation model+ In this application, the VC property is hard to establish for the projection class of interest but easy to establish for the other projection class

Generalized Transform Analysis of Affine Processes and Applications in Finance

Nonlinearity is an important consideration in many problems of finance and economics, such as pricing securities and solving equilibrium models. This article provides analytical treatment of a general class of nonlinear transforms for processes with tractable conditional characteristic functions. We extend existing results on characteristic function-based transforms to a substantially wider class of nonlinear functions while maintaining low dimensionality by avoiding the need to compute the density function. We illustrate the applications of the generalized transform in pricing defaultable bonds with stochastic recovery. We also use the method to analytically solve a class of general equilibrium models with multiple goods and apply this model to study the effects of time-varying labor income risk on the equity premium

A New Perspective on Gaussian Dynamic Term Structure Models

In any canonical Gaussian dynamic term structure model (GDTSM), the conditional forecasts of the pricing factors are invariant to the imposition of no-arbitrage restrictions. This invariance is maintained even in the presence of a variety of restrictions on the factor structure of bond yields. To establish these results, we develop a novel canonical GDTSM in which the pricing factors are observable portfolios of yields. For our normalization, standard maximum likelihood algorithms converge to the global optimum almost instantaneously. We present empirical estimates and out-of-sample forecasts for several GDTSMs using data on U.S. Treasury bond yields

Rare Disasters and Risk Sharing with Heterogeneous Beliefs

Although the threat of rare economic disasters can have large effect on asset prices, difficulty in inference regarding both their likelihood and severity provides the potential for disagreements among investors. Such disagreements lead investors to insure each other against the types of disasters each one fears the most. Due to the highly nonlinear relationship between consumption losses in a disaster and the risk premium, a small amount of risk sharing can significantly attenuate the effect that disaster risk has on the equity premium. We characterize the sensitivity of risk premium to wealth distribution analytically. Our model shows that time variation in the wealth distribution and the amount of disagreement across agents can both lead to significant variation in disaster risk premium. It also highlights the conditions under which disaster risk premium will be large, namely when disagreement across agents is small or when the wealth distribution is highly concentrated in agents fearful of disasters. Finally, the model predicts an inverse U-shaped relationship between the equity premium and the size of the disaster insurance market.

Rare Disasters and Risk Sharing with Heterogeneous Beliefs

Risks of rare economic disasters can have a large impact on asset prices. At the same time, difficulties in inference regarding both the likelihood and severity of disasters, as well as agency problems, can lead to significant disagreements among investors about disaster risk. We show that such disagreements generate strong risk-sharing motives, such that just a small number of optimists in the economy will significantly reduce the disaster risk premium. Our model highlights the “latent” nature of disaster risk. The disaster risk premium will likely be low and smooth during normal times but increases dramatically when the risk-sharing capacity of the optimists is reduced, e.g., following a disaster. The model also helps reconcile the difference in the amount of disaster risk implied by financial markets and international macroeconomic data, and provides caution to the approach of extracting disaster probabilities from asset prices, which will disproportionately reflect the beliefs of a small group of optimists. Finally, our model predicts an inverse U-shaped relation between the equity premium and the size of the disaster insurance market

Effect of moisture on leaf litter decomposition and its contribution to soil respiration in a temperate forest

The degree to which increased soil respiration rates following wetting is caused by plant (autotrophic) versus microbial (heterotrophic) processes, is still largely uninvestigated. Incubation studies suggest microbial processes play a role but it remains unclear whether there is a stimulation of the microbial population as a whole or an increase in the importance of specific substrates that become available with wetting of the soil. We took advantage of an ongoing manipulation of leaf litter <sup>14</sup>C contents at the Oak Ridge Reservation, Oak Ridge, Tennessee, to (1) determine the degree to which an increase in soil respiration rates that accompanied wetting of litter and soil, following a short period of drought, could be explained by heterotrophic contributions; and (2) investigate the potential causes of increased heterotrophic respiration in incubated litter and 0–5 cm mineral soil. The contribution of leaf litter decomposition increased from 6 ± 3 mg C m<sup>−2</sup> hr<sup>−1</sup> during a transient drought, to 63 ± 18 mg C m<sup>−2</sup> hr<sup>−1</sup> immediately after water addition, corresponding to an increase in the contribution to soil respiration from 5 ± 2% to 37 ± 8%. The increased relative contribution was sufficient to explain all of the observed increase in soil respiration for this one wetting event in the late growing season. Temperature (13°C versus 25°C) and moisture (dry versus field capacity) conditions did not change the relative contributions of different decomposition substrates in incubations, suggesting that more slowly cycling C has at least the same sensitivity to decomposition as faster cycling organic C at the temperature and moisture conditions studied