We determine the magnetic penetration depth λ(T) in superconducting films by measuring the mutual inductance of two coils located on opposite sides of the films. The apparatus is designed to produce an accurate value for λ(0) without any assumptions about the dependence of λ(T/Tc)/λ(0) on T/Tc. In a typical configuration of coils and a 100±10 nm thick by 6 mm radius film, λ can be measured to better than ±12% as long as λ≳1500 Å. The noise level is typically ±2 Å. If two films are made the same way, so that they have the same thickness d, and they are measured in the same apparatus, then the relative uncertainty in λ between the two films is only ±9%, because uncertainties in d, the coil dimensions, etc., are eliminated. This article describes the apparatus and a detailed numerical model which illustrates the induced current density in the film and establishes the sources of uncertainties. The accuracy of the model is demonstrated through comparison with measurements on 0.15 mm thick circular Pb disks.

ABSTRACT.The theoretical literature has a rich characterization of scoring rules for eliciting the subjective beliefs that an individual has for continuous events, but under the restrictive assumption of risk neutrality. It is well known that risk aversion can dramatically affect the incentives to correctly report the true subjective probability of a binary event. Alternatively, one must carefully calibrate inferences about true subjective probabilities from elicited subjective probabilities over binary events, recognizing the incentives that risk averse agents have to report the same probability for the two outcomes and reduce the variability of payoffs from the scoring rule. We characterize the comparable implications of the general case of a risk averse agent when facing a popular scoring rule over continuous events, and find that these concerns do not apply with anything like the same force. For empirically plausible levels of risk aversion, one can reliably elicit most important features of the latent subjective belief distribution without undertaking calibration for risk attitudes. †

The penetration depth k(T) in YBa2(Cu& "M )307 films, with M=Ni or Zn and nominal concentrations, 0.02~x~0.06, is obtained from the mutual inductance of coaxial coils on opposite sides of the films. Both Ni and Zn increase A, (0) very rapidly, such that the superAuid density, n, (0) cc A, (0), decreases by a factor of 2 for each percent of dopant. The rapid increase in A, (0) implies that disorder fills in the superconducting density of states at low energy, so that Ns(0) is roughly 80 -95 % of the normalstate density of states. An analytic d-wave theory, valid at T =0, finds that A, (0) increases rapidly with disorder, but not as rapidly as observed. It is striking that the dependence of A, ( T/T, ) on T!T, does not change significantly as x increases from 2% to 6%, although it is different from undoped YBa2Cu307films. An ad hoc phenomenological model finds that one should expect this result. Finally, the values of Ns(0) deduced from A, are somewhat larger than values deduced from specific-heat measurements on Zn-doped YBa2Cu307 z, which also indicate increasing gaplessness with doping.

Variable annuity contracts frequently have many options and option-like features embedded in the contracts. Some are obvious, such as guaranteed minimum death benefits (GMDBs), while others are less obviously option-like. In this article, we consider the effect of the real option to transfer funds between fixed and variable accounts. If a GMDB rider is considered in isolation, it is sometimes in the policyholder's interest to transfer to the fixed fund if the fixed fund earns less than the variable fund in a risk-neutral world. On the other hand, the option to transfer will not be used if the entire annuity and rider are considered together. Copyright The Journal of Risk and Insurance, 2006.

Much attention has been focused recently on the issue of valuing guaranteed minimum death benefits embedded in annuity contracts. These benefits resemble a sequence of put options and their value should obey a differential equation similar to the Black-Scholes equation for simple put options. This paper derives a number of analytic solutions to this equation for a number of simple mortality laws.