Bid and Ask Asset Pricing Through the Extended Gini Premium Principle : Sufficient and Necessary Conditions for Trading

Since Shalit and Yitzhaki (1984) the premium principle based on the Extended Gini of an uncertain position has been defined as its expected value minus the extended Gini index. We propose this principle for making capital asset pricing tailored to the investor profile. Bid and ask prices of the counter-parties involved in transactions are defined. Risk and gain-premiaare given through "personalized" Extended Gini indices able to capture the buyer risk aversion and the seller gain propension. Sufficient and necessary conditions for trading are set out. Closed-end formulae for the most common asset distributions used in Finance are given and general guide-lines involving the asset skewness drawn. Eventually, we discuss the optimal bid and ask portfolio allocation. We give evidence that if the portfolio distributions are symmetrical and/or the traders have a "moderate" profile the optimal bid-portfolio corresponds always to the worst ask-portfolio. Vice versa, if portfolio distributions are asymmetrical and the traders have an "extreme profile", i.e. strongly risk-averse and highly gain-prone, then optimal bid and ask portfolios are not related