The dependence structure of the life statuses plays an important role in the valuation of life insurance products involving multiple lives. Although the mortality of individuals is well studied in the literature, their dependence remains a challenging field. In this paper, the main objective is to introduce a new approach for analyzing the mortality dependence between two individuals in a couple. It is intended to describe in a dynamic framework the joint mortality of married couples in terms of marginal mortality rates. The proposed framework is general and aims to capture, by adjusting some parametric form, the desired effect such as the “broken-heart syndrome”. To this end, we use a well-suited multiplicative decomposition, which will serve as a building block for the framework to relate the dependence structure and the marginals, and we make the link with existing practice of affine mortality models. Finally, given that the framework is general, we propose some illustrative examples and show how the underlying model captures the main stylized facts of bivariate mortality dynamics.
Herein, we report the total synthesis of traumatic lactone and rhizobialide by utilizing allenoic acid to construct the lactone ring. The key starting materials, allenoic acids, could be prepared by the ATA (allenation of terminal alkynes) of a terminal alkyne with an aldehyde that contained a protected hydroxyl group followed by hydrolysis. Importantly, the asymmetric synthesis could be realized just by replacing racemic diphenylprinol with (R)- or (S)-diphenylprinol to deliver the optically active allenoate. 相似文献
A CuI-catalyzed Suzuki cross-coupling reaction of organoboron derivatives with alkynyl bromides has been developed. In the presence of CuI (10 mol %) and 8-hydroxyquinoline (20 mol %), organoboron derivatives including aromatic and alkenyl boronic acids, potassium aryltrifluoroborates, and sodium tetraphenylborate reacted smoothly with 1-bromo-2-substituted acetylene to generate the corresponding cross-coupling products in good to excellent yields in C2H5OH. It is important to note that aromatic N,O-ligand 8-hydroxyquinoline is the most effective ligand for the reaction. 相似文献