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

Quantum nondemolition measurement of mechanical motion quanta

The fields of opto- and electromechanics have facilitated numerous advances in the areas of precision measurement and sensing, ultimately driving the studies of mechanical systems into the quantum regime. To date, however, the quantization of the mechanical motion and the associated quantum jumps between phonon states remains elusive. For optomechanical systems, the coupling to the environment was shown to preclude the detection of the mechanical mode occupation, unless strong single photon optomechanical coupling is achieved. Here, we propose and analyse an electromechanical setup, which allows to overcome this limitation and resolve the energy levels of a mechanical oscillator. We find that the heating of the membrane, caused by the interaction with the environment and unwanted couplings, can be suppressed for carefully designed electromechanical systems. The results suggest that phonon number measurement is within reach for modern electromechanical setups.Comment: 8 pages, 5 figures plus 24 pages, 11 figures supplemental materia

Optomechanical creation of magnetic fields for photons on a lattice

We propose using the optomechanical interaction to create artificial magnetic fields for photons on a lattice. The ingredients required are an optomechanical crystal, i.e. a piece of dielectric with the right pattern of holes, and two laser beams with the right pattern of phases. One of the two proposed schemes is based on optomechanical modulation of the links between optical modes, while the other is an lattice extension of optomechanical wavelength-conversion setups. We illustrate the resulting optical spectrum, photon transport in the presence of an artificial Lorentz force, edge states, and the photonic Aharonov-Bohm effect. Moreover, wWe also briefly describe the gauge fields acting on the synthetic dimension related to the phonon/photon degree of freedom. These can be generated using a single laser beam impinging on an optomechanical array

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

Quantum techniques using continuous variables of light

We present schemes for the generation and evaluation of continuous variable entanglement of bright optical beams and give a brief overview of the variety of optical techniques and quantum communication applications on this basis. A new entanglement-based quantum interferometry scheme with bright beams is suggested. The performance of the presented schemes is independent of the relative interference phase which is advantageous for quantum communication applications.Comment: 11 pages, 5 figures; minor correction, accepted versio

Introduction to Quantum Noise, Measurement and Amplification

The topic of quantum noise has become extremely timely due to the rise of quantum information physics and the resulting interchange of ideas between the condensed matter and AMO/quantum optics communities. This review gives a pedagogical introduction to the physics of quantum noise and its connections to quantum measurement and quantum amplification. After introducing quantum noise spectra and methods for their detection, we describe the basics of weak continuous measurements. Particular attention is given to treating the standard quantum limit on linear amplifiers and position detectors using a general linear-response framework. We show how this approach relates to the standard Haus-Caves quantum limit for a bosonic amplifier known in quantum optics, and illustrate its application for the case of electrical circuits, including mesoscopic detectors and resonant cavity detectors.Comment: Substantial improvements over initial version; include supplemental appendices

A many-fermion generalization of the Caldeira-Leggett model

We analyze a model system of fermions in a harmonic oscillator potential under the influence of a dissipative environment: The fermions are subject to a fluctuating force deriving from a bath of harmonic oscillators. This represents an extension of the well-known Caldeira-Leggett model to the case of many fermions. Using the method of bosonization, we calculate one- and two-particle Green's functions of the fermions. We discuss the relaxation of a single extra particle added above the Fermi sea, considering also dephasing of a particle added in a coherent superposition of states. The consequences of the separation of center-of-mass and relative motion, the Pauli principle, and the bath-induced effective interaction are discussed. Finally, we extend our analysis to a more generic coupling between system and bath, that results in complete thermalization of the system.Comment: v3: fixed pdf problem; v2: added exact formula (Eq. 42) for Green's function and discussion of equilibrium density matrix (new Fig. 2); 10 figures, 21 pages, see quant-ph/0305098 for brief version of some of these result

Reduction of Guided Acoustic Wave Brillouin Scattering in Photonic Crystal Fibers

Guided Acoustic Wave Brillouin Scattering (GAWBS) generates phase and polarization noise of light propagating in glass fibers. This excess noise affects the performance of various experiments operating at the quantum noise limit. We experimentally demonstrate the reduction of GAWBS noise in a photonic crystal fiber in a broad frequency range using cavity sound dynamics. We compare the noise spectrum to the one of a standard fiber and observe a 10-fold noise reduction in the frequency range up to 200 MHz. Based on our measurement results as well as on numerical simulations we establish a model for the reduction of GAWBS noise in photonic crystal fibers.Comment: 4 pages, 7 figures; added numerical simulations, added reference

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