Types of dependence and time-dependent association between two lifetimes in single parameter copula models

Most publications on modeling insurance contracts on two lives, assuming dependence of the two lifetimes involved, focus on the time of inception of the contract. The dependence between the lifetimes is usually modeled through a copula and the effect of this dependence on the pricing of a joint life policy is measured. This paper investigates the effect of association at the outset on the mortality in the future. The conditional law of mortality of an individual, given his survival and given the life status of the partner is derived. The conditional joint survival distribution of a couple at any duration, given that the two lives are then alive, is also derived. We analyze how the degree of dependence between the two members of a couple varies throughout the duration of a contract. We will do that for (mainly Archimedean) copula models, with one parameter for the degree of dependence. The conditional distributions hence derived provide the basis for the calculation of prospective provisions

Archimedean copulas derived from Morgenstern utility functions

The (additive) generator of an Archimedean copula - as well as the inverse of the generator - is a strictly decreasing and convex function, while Morgenstern utility functions (applying to risk averse decision makers) are nondecreasing and concave. This provides a basis for deriving either a generator of Archimedean copulas, or its inverse, from a Morgenstern utility function. If we derive the generator in this way, dependence properties of an Archimedean copula that are often taken to be desirable, match with generally sought after properties of the corresponding utility function. It is shown how well known copula families are derived from established utility functions. Also, some new copula families are derived, and their properties are discussed. If, on the other hand, we instead derive the inverse of the generator from the utility function, there is a link between the magnitude of measures of risk attitude (like the very common Arrow-Pratt coefficient of absolute risk aversion) and the strength of dependence featured by the corresponding Archimedean copula

The probationary period as a screening device: competitive markets

Seminal papers about asymmetry of information in a competitive insurance market, and the monetary deductible as a screening device show that any existing equilibrium is of a separating type. High risks buy complete insurance whilst low risks buy partial insurance. Rothschild and Stiglitz (1976) deal with insurance companies showing Nash behaviour, while Miyazaki (1977) and Spence (1978) consider firms with Wilson foresight. In this paper, we analyze the strength of the probationary period as a screening device. We show that in such a case a) under Nash behavior, low risks may prefer not to purchase any insurance at all in equilibrium and b)under Wilson foresight, a pooling equilibrium may exist

Evolution of coupled lives' dependency across generations and pricing impact

This paper studies the dependence between coupled lives - both within and across generations - and its effects on prices of reversionary annuities in the presence of longevity risk. Longevity risk is represented via a stochastic mortality intensity. Dependence is modelled through copula functions. We consider Archimedean single and multi-parameter copulas. We and that dependence decreases when passing from older generations to younger generations. Not only the level of dependence but also its features - as measured by the copula - change across generations: the best-fit Archimedean copula is not the same across generations. Moreover, for all the generations under exam the single-parameter copula is dominated by the two-parameter one. The independence assumption produces quantifiable mispricing of reversionary annuities. The misspecification of the copula produces different mispricing effects on different generations. The research is conducted using a well-known dataset of double life contracts

Sensitive Absorption Imaging of Single Atoms in Front of a Mirror

In this paper we show that the sensitivity of absorption imaging of ultracold atoms can be significantly improved by imaging in a standing-wave configuration. We present simulations of single-atom absorption imaging both for a travelling-wave and a standing-wave imaging setup, based on a scattering approach to calculate the optical density of a single atom. We find that the optical density of a single atom is determined only by the numerical aperture of the imaging system. We determine optimum imaging parameters, taking all relevant sources of noise into account. For reflective imaging we find an improvement of 1.7 in the maximum signal-to-noise ratio can be achieved. This is particularly useful for imaging in the vicinity of an atom chip, where a reflective surface is naturally present

Topological constraints on magnetostatic traps

We theoretically investigate properties of magnetostatic traps for cold atoms that are subject to externally applied uniform fields. We show that Ioffe Pritchard traps and other stationary points of $B$ are confined to a two-dimensional curved manifold defined by $\det(\partial B_i/\partial x_j)=0$. We describe how stationary points can be moved over the manifold by applying external uniform fields. The manifold also plays an important role in the behavior of points of zero field. Field zeroes occur in two distinct types, in separate regions of space divided by the manifold. Pairs of zeroes of opposite type can be created or annihilated on the manifold. Finally, we give examples of the manifold for cases of practical interest.Comment: 7 pages, 5 figure

Predicting low-frequency radio fluxes of known extrasolar planets

Context. Close-in giant extrasolar planets (''Hot Jupiters'') are believed to be strong emitters in the decametric radio range. Aims. We present the expected characteristics of the low-frequency magnetospheric radio emission of all currently known extrasolar planets, including the maximum emission frequency and the expected radio flux. We also discuss the escape of exoplanetary radio emission from the vicinity of its source, which imposes additional constraints on detectability. Methods. We compare the different predictions obtained with all four existing analytical models for all currently known exoplanets. We also take care to use realistic values for all input parameters. Results. The four different models for planetary radio emission lead to very different results. The largest fluxes are found for the magnetic energy model, followed by the CME model and the kinetic energy model (for which our results are found to be much less optimistic than those of previous studies). The unipolar interaction model does not predict any observable emission for the present exoplanet census. We also give estimates for the planetary magnetic dipole moment of all currently known extrasolar planets, which will be useful for other studies. Conclusions. Our results show that observations of exoplanetary radio emission are feasible, but that the number of promising targets is not very high. The catalog of targets will be particularly useful for current and future radio observation campaigns (e.g. with the VLA, GMRT, UTR-2 and with LOFAR).Comment: 4 figures; Table 1 is available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/475/35