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

Sonoelastography of the Common Flexor Tendon of the Elbow with Histologic Agreement: A Cadaveric Study.

Purpose To determine the correlation of the results of conventional B-mode ultrasonography (US) and compression sonoelastography with histologic results in common flexor tendons of the elbow in human cadavers. Materials and Methods Twenty-five common flexor tendons were evaluated in 16 fresh, unembalmed cadavers of 11 women with a median age of 85 years (range, 71-101 years) and five men with a median age of 78 years (range, 70-88 years). Informed consent was provided according to the last will of the donors. B-mode US results were classified as grade 1, normal tendon with homogeneous fibrillar pattern; grade 2, tendon thickening or hypoechoic areas and/or calcifications in less than 30% of the tendon; or grade 3, hypoechoic areas and/or calcifications greater than 30% of the tendon. Sonoelastographic results were grade 1, blue (hardest) to green (hard); grade 2, yellow (soft); and grade 3, red (softest). The intraclass correlation coefficient was calculated to determine agreement with histologic findings for each B-mode US, sonoelastographic, and combined B-mode US and sonoelastographic examination. Histologic results were grade 1, normal, with parallel fibrillar pattern; grade 2, mild tendinopathy, with cellular infiltration, angiogenesis, or fatty vacuoles; or grade 3, severe tendinopathy, with loss of parallel collagen structure and necrosis. Results Histologic alterations were detected in 44% (11 of 25) of biopsy specimens. Intraclass correlation with histologic results was 0.57 for B-mode US, 0.68 for sonoelastography, and 0.84 for the combination of the two approaches. Conclusion The addition of sonoelastography to B-mode US provided statistically significant improvement in correlation with histologic results compared with the use of B-mode US alone (P \u3c .02). (©) RSNA, 2016 Online supplemental material is available for this article

Accounting for risk of non linear portfolios: a novel Fourier approach

The presence of non linear instruments is responsible for the emergence of non Gaussian features in the price changes distribution of realistic portfolios, even for Normally distributed risk factors. This is especially true for the benchmark Delta Gamma Normal model, which in general exhibits exponentially damped power law tails. We show how the knowledge of the model characteristic function leads to Fourier representations for two standard risk measures, the Value at Risk and the Expected Shortfall, and for their sensitivities with respect to the model parameters. We detail the numerical implementation of our formulae and we emphasizes the reliability and efficiency of our results in comparison with Monte Carlo simulation.Comment: 10 pages, 12 figures. Final version accepted for publication on Eur. Phys. J.

A positive tensor network approach for simulating open quantum many-body systems

Open many-body quantum systems play an important role in quantum optics and condensed-matter physics, and capture phenomena like transport, interplay between Hamiltonian and incoherent dynamics, and topological order generated by dissipation. We introduce a versatile and practical method to numerically simulate one-dimensional open quantum many-body dynamics using tensor networks. It is based on representing mixed quantum states in a locally purified form, which guarantees that positivity is preserved at all times. Moreover, the approximation error is controlled with respect to the trace norm. Hence, this scheme overcomes various obstacles of the known numerical open-system evolution schemes. To exemplify the functioning of the approach, we study both stationary states and transient dissipative behaviour, for various open quantum systems ranging from few to many bodies.Comment: 13 pages, 7 figures, significant material on error bounds adde

Multivariate risks and depth-trimmed regions

We describe a general framework for measuring risks, where the risk measure takes values in an abstract cone. It is shown that this approach naturally includes the classical risk measures and set-valued risk measures and yields a natural definition of vector-valued risk measures. Several main constructions of risk measures are described in this abstract axiomatic framework. It is shown that the concept of depth-trimmed (or central) regions from the multivariate statistics is closely related to the definition of risk measures. In particular, the halfspace trimming corresponds to the Value-at-Risk, while the zonoid trimming yields the expected shortfall. In the abstract framework, it is shown how to establish a both-ways correspondence between risk measures and depth-trimmed regions. It is also demonstrated how the lattice structure of the space of risk values influences this relationship.Comment: 26 pages. Substantially revised version with a number of new results adde

Template-Directed Ligation of Tethered Mononucleotides by T4 DNA Ligase for Kinase Ribozyme Selection

Background: In vitro selection of kinase ribozymes for small molecule metabolites, such as free nucleosides, will require partition systems that discriminate active from inactive RNA species. While nucleic acid catalysis of phosphoryl transfer is well established for phosphorylation of 59 or 29 OH of oligonucleotide substrates, phosphorylation of diffusible small molecules has not been demonstrated. Methodology/Principal Findings: This study demonstrates the ability of T4 DNA ligase to capture RNA strands in which a tethered monodeoxynucleoside has acquired a 59 phosphate. The ligation reaction therefore mimics the partition step of a selection for nucleoside kinase (deoxy)ribozymes. Ligation with tethered substrates was considerably slower than with nicked, fully duplex DNA, even though the deoxynucleotides at the ligation junction were Watson-Crick base paired in the tethered substrate. Ligation increased markedly when the bridging template strand contained unpaired spacer nucleotides across from the flexible tether, according to the trends: A2.A1.A3.A4.A0.A6.A8.A10 and T2.T3.T4.T6<T1.T8.T10. Bridging T’s generally gave higher yield of ligated product than bridging A’s. ATP concentrations above 33 mM accumulated adenylated intermediate and decreased yields of the gap-sealed product, likely due to re-adenylation of dissociated enzyme. Under optimized conditions, T4 DNA ligase efficiently (.90%) joined a correctly paired, or T:G wobble-paired, substrate on the 39 side of the ligation junction while discriminating approximately 100-fold against most mispaire

Optimization of fixation methods for observation of bacterial cell morphology and surface ultrastructures by atomic force microscopy

Fixation ability of five common fixation solutions, including 2.5% glutaraldehyde, 10% formalin, 4% paraformaldehyde, methanol/acetone (1:1), and ethanol/acetic acid (3:1) were evaluated by using atomic force microscopy in the present study. Three model bacteria, i.e., Escherichia coli, Pseudomonas putida, and Bacillus subtilis were applied to observe the above fixation methods for the morphology preservation of bacterial cells and surface ultrastructures. All the fixation methods could effectively preserve cell morphology. However, for preserving bacterial surface ultrastructures, the methods applying aldehyde fixations performed much better than those using alcohols, since the alcohols could detach the surface filaments (i.e., flagella and pili) significantly. Based on the quantitative and qualitative assessments, the 2.5% glutaraldehyde was proposed as a promising fixation solution both for observing morphology of both bacterial cell and surface ultrastructures, while the methonal/acetone mixture was the worst fixation solution which may obtain unreliable results