Tail VaR Measures in a Multi-period Setting

Abstract

This paper studies a coherent acceptability measure which is a negative coherent risk measure, in a multi-period model. When a coherent acceptability measure changes according to new information in the market, a time consistency plays an important role. The usual strong time consistency gives too severe a multi-period Tail Value at Risk (Tail VaR) from a practical viewpoint. We study a weak type of time consistency and propose new multi-period Tail VaR measures.     

The 2-twist-spun trefoil has the triple point number four

The triple point number of an embedded surface in 4-space is the minimal number of the triple points on all the projection images into 3-space. We show that the 2-twist-spun trefoil has the triple point number four.

     

Diffusion-weighted imaging of local recurrent prostate cancer after radiation therapy: comparison with 22-core three-dimensional prostate mapping biopsy

Accurate localization of local recurrence within the prostate gland is important to perform focal salvage therapy effectively with minimal complications. The purpose of this study was to evaluate the usefulness of diffusion-weighted imaging (DWI) in the detection and localization of prostate cancer recurrence in patients with biochemical failure after definitive radiation therapy using 22-core three-dimensional prostate mapping biopsy (3D-PMB) as a standard reference. Ten patients who underwent magnetic resonance imaging and 22-core 3D-PMB were retrospectively analyzed. For visual assessment of DWI, the prostate was divided into 22 regions corresponding to 3D-PMB. Two diagnostic radiologists determined the presence of abnormal high signal intensity in each region on DWI, and the results of DWI were compared with those of 3D-PMB. Of the 220 regions, 16 regions in six patients were positive for cancer on 3D-PMB, and 30 regions in six patients were judged as positive on DWI. On a patient-by-patient basis, sensitivity and specificity were 100% (6/6) and 100% (4/4), respectively. On a region-by-region basis, sensitivity, specificity, positive predictive value, negative predictive value and accuracy were 69% (11/16), 91% (185/204), 37% (11/30), 97% (185/190) and 89% (196/220), respectively. For discrepant localization between DWI and pathology, DWI-positive and pathology-positive regions tended to be adjacent to each other. In conclusion, DWI is a useful tool for the detection and localization of recurrent prostate cancer in patients with biochemical failure after radiation therapy and may be helpful in the planning of focal salvage therapy.     

Polyaddition of bifunctional cyclic carbonate with diamine in ionic liquids: In situ ion composite formation and simple separation of ionic liquid

Polyaddition of bifunctional cyclic carbonates and diamines in ionic liquids proceeded smoothly to afford polyurethanes having hydroxyl groups in the side chain (i.e., poly(hydroxyurethane)). The reaction mixtures separated into ionic liquids and ionic composites consisting of poly(hydroxyurethane) and ionic liquids. The ionic composites originated from the interactions between hydroxyl groups in the side chains and the ionic liquids, confirmed by IR spectroscopic analysis. When the polyaddition was conducted in the mixed solvent consists of water and N‐n‐butylimidazolium hexafluorophosphate. After the reaction, the polymer and the ionic liquid could be separated easily. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 4629–4635, 2009     

LCST‐type liquid–liquid and liquid–solid phase transition behaviors of hyperbranched polyglycerol bearing imidazolium salt

A hyperbranched polyglycerol bearing imidazolium tosylate units ( ITHB ) was synthesized through the imidazolium salt‐modification of hyperbranched polyglycerol ( HB ). ITHB was found to possess novel reversible lower critical solution temperature (LCST)‐type liquid–liquid and liquid–solid phase transition behaviors in a methanol/chloroform mixed solution. The phase transition temperatures of the liquid–liquid phase transition (PTT_1to2) and liquid–solid phase transition (PTT_2toSus) increased with increasing the ratio of methanol in the mixed solution and decreasing the concentration of ITHB . Additionally, increasing the molecular weight of ITHB decreased the PTT values. The liquid–liquid phase transition was caused by the aggregation of ITHB , which was proved by dynamic light scattering measurement. In contrast, the liquid–solid phase transition was caused by the solvation cleavage between the imidazolium rings and solvents, which was proved by ¹H NMR measurement. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2009