Asset-liability management is a means of managing the risk that can arise from the changes in the relationship between assets and liabilities. Value-at-risk (VaR) and tail conditional expectation (TCE) have also emerged in recent years as standard tools for measuring and controlling the risk of trading portfolios. In some dynamical settings however, the limits of TCE can be transformed into the limits of VaR and conversely even though TCE is more preferable to VaR since it is coherent and VaR is not. In this paper we obtain the optimal price of an institution’s assets- liabilities under the TCE with no transaction cost.
In the framework of gravitational theory of general relativity, this article has systematically and radically solved the problem of galaxy formation and some significant cosmological puzzles. A flaw with Einstein’s equation of gravitational field is firstly corrected and the foundations of general relativity are perfected and developed, and space-time is proved to be infinite, expansion and contraction of universe are proved to be in circles, the singular point of big bang is naturally eliminated, celestial bodies and galaxies are proved growing up with cosmic expansion, for example Earth’s mass and radius at present increase by 1.2 trillion tons and 0.45mm, respectively in a year, in response to which geostationary satellites rise by 2.7mm.