Valuing Guaranteed Minimum Death Benefit Options in Variable Annuities Under a Benchmark Approach

Variable annuities (VAs) represent a marked change from earlier life products in the guarantees that they offer and it is no longer possible to manage the risks of these liabilities using traditional actuarial methods. Thinking about guarantees as options suggests applying risk neutral pricing in order to value the embedded guarantees, such as guaranteed minimum death benefits (GMDBs). However, due to the long maturities of contracts, stochastic volatility and many other reasons, VA markets are incomplete. In this paper we propose a methodology for pricing GMDBs under a benchmark approach which does not require the existence of a risk neutral probability measure. We assume that the insurance company invests in the growth optimal portfolio of its investment universe and apply real world pricing rather than risk neutral pricing. In particular, we consider the minimal market model and conclude that in this setup the fair price of a roll-up GMDB is lower than the price obtained by applying standard risk neutral pricing. Moreover, we take into account rational as well as irrational lapsation of the policyholder.Benchmark approach; fair pricing; GMDB; growth optimal portfolio; lapsation; local volatility function; minimal market model; variable annuities

Remark on the anisotropic prescribed mean curvature equation on arbitrary domains

In this article we consider the Dirichlet problem for hypersurfaces of aniso- tropic prescribed mean curvature H = H(x, u, N) depending on $${x \in \varOmega \subset \mathbb {R}^n}$$, the height u of the hypersurface M = graph u over $${\varOmega}$$ and the unit normal N to M at (x, u). We give a condition relating H and the mean curvature of $${\partial \varOmega}$$ that guarantees the existence of smooth solutions even for not necessarily convex domains

Fermionic Mach-Zehnder interferometer subject to a quantum bath

We study fermions in a Mach-Zehnder interferometer, subject to a quantum-mechanical environment leading to inelastic scattering, decoherence, renormalization effects, and time-dependent conductance fluctuations. Both the loss of interference contrast as well as the shot noise are calculated, using equations of motion and leading order perturbation theory. The full dependence of the shot-noise correction on setup parameters, voltage, temperature and the bath spectrum is presented. We find an interesting contribution due to correlations between the fluctuating renormalized phase shift and the output current, discuss the limiting behaviours at low and high voltages, and compare with simpler models of dephasing.Comment: 5 pages, 3 figure

Defining French ‘Romanesque’: the Zodiaque series

This essay examines the use of the term “Romanesque” as an artistic style and time period for architecture, sculpture and other arts photographed and published in a journal and multiple series of books by monks at the abbey of la Pierre-qui-Vire in Burgundy between 1951 and 2001. Although the term suggests a coherent body of work with related qualities, the actual imagery destabilizes our understanding of how one can actually define Romanesque. At the same time, the artfully composed photogravure illustrations and inclusive survey of sites strongly influenced art historians of the twentieth century by reinforcing notions of geographic workshops, bringing a fresh, modernist aesthetic to well known material, and publishing photographs of many unknown works for the first time

The effect of the helicotrema on low-frequency loudness perception

Below approximately 40 Hz, the cochlear travelling wave reaches the apex, and differential pressure is shunted through the helicotrema, reducing hearing sensitivity. Just above this corner frequency, a resonance feature is often observed in objectively measured middle-ear-transfer functions (METFs). This study inquires whether overall and fine structure characteristics of the METF are also perceptually evident. Equal-loudness-level contours (ELCs) were measured between 20 and 160 Hz for 14 subjects in a purpose-built test chamber. In addition, the inverse shapes of their METFs were obtained by adjusting the intensity of a low-frequency suppressor tone to maintain an equal suppression depth of otoacoustic emissions for various suppressor tone frequencies (20–250 Hz). For 11 subjects, the METFs showed a resonance. Six of them had coinciding features in both ears, and also in their ELC. For two subjects only the right-ear METF was obtainable, and in one case it was consistent with the ELC. One other subject showed a consistent lack of the feature in their ELC and in both METFs. Although three subjects displayed clear inconsistencies between both measures, the similarity between inverse METF and ELC for most subjects shows that the helicotrema has a marked impact on low-frequency sound perception

Optomechanical cooling of levitated spheres with doubly-resonant fields

Optomechanical cooling of levitated dielectric particles represents a promising new approach in the quest to cool small mechanical resonators towards their quantum ground state. We investigate two-mode cooling of levitated nanospheres in a self-trapping regime. We identify a rich structure of split sidebands (by a mechanism unrelated to usual strong-coupling effects) and strong cooling even when one mode is blue detuned. We show the best regimes occur when both optical fields cooperatively cool and trap the nanosphere, where cooling rates are over an order of magnitude faster compared to corresponding single-sideband cooling rates.Comment: 8 Pages, 7 figure

Enhanced quantum nonlinearities in a two mode optomechanical system

In cavity optomechanics, nanomechanical motion couples to a localized optical mode. The regime of single-photon strong coupling is reached when the optical shift induced by a single phonon becomes comparable to the cavity linewidth. We consider a setup in this regime comprising two optical modes and one mechanical mode. For mechanical frequencies nearly resonant to the optical level splitting, we find the photon-phonon and the photon-photon interactions to be significantly enhanced. In addition to dispersive phonon detection in a novel regime, this offers the prospect of optomechanical photon measurement. We study these QND detection processes using both analytical and numerical approaches