A natural value unit—Econophysics as arbiter between finance and economics

Foreign exchange markets show that currency units (= accounting or nominal price units) are variables. Technical and economic progress evidences that the consumer baskets (= purchasing power units or real price units) are also variables. In contrast, all physical measurement units are constants and either defined in the SI (=metric) convention or based upon natural constants (= “natural” or Planck units). Econophysics can identify a constant natural value scale or value unit (natural numeraire) based upon Planck energy. In honor of the economist L. Walras, this “Planck value” could be called Walras (Wal), thereby using the SI naming convention. One Wal can be shown to have a physiological and an economic interpretation in that it is equal to the annual minimal real cost of physiological life of a reference person at minimal activity. The price of one Wal in terms of any currency can be estimated by hedonic regression techniques used in inflation measurement (axiometry). This pilot research uses official disaggregated Swiss Producer and Consumer Price Index (PPI and CPI) data and estimates the hedonic Walras price (HWP), quoted in Swiss francs in 2003, and its inverse, the physical purchasing power (PhPP) of the Swiss franc in 2003.     

Risk measures on ordered non-reflexive Banach spaces

This work is devoted to the study of coherent and convex risk measure on non-reflexive Banach spaces. An extension of dual representation and continuity results which hold in the case of reflexive spaces is established in this paper for the class of non-reflexive Banach spaces. This study also relies on the fact that the riskless bond is replaced by some numeraire asset which defines a base on the cone of the spot-price functionals.     

分数布朗运动环境下的期权定价与测度变换

研究分数B-S市场中的期权定价问题.通过选取不同的资产作为计价单位及相应的测度变换,将经典模型中的计价单位变换方法推广到分数布朗运动市场环境,既丰富了分数期权定价的拟鞅方法,也得到了分数期权定价公式的新的推导方法.