Linear price systems, typically used to model ââ?¬Å?perfectââ?¬Â markets, are widely known not to accommodate\nmost of the typical frictions featured in ââ?¬Å?actualââ?¬Â ones. Since some years, ââ?¬Å?proportionalââ?¬Â\nfrictions (taxes, bid-ask spreads, and so on) are modeled by means of sublinear price functionals,\nwhich proved to give a more ââ?¬Å?realisticââ?¬Â description. In this paper, we want to introduce two more\nclasses of functionals, not yet widely used in Mathematical Finance, which provide a further improvement\nand an even closer adherence to actual markets, namely the class of granular functionals,\nobtained when the unit prices of traded assets are increasing w.r.t. the traded amount; and\nthe class of star-shaped functionals, obtained when the average unit prices of traded assets are increasing\nw.r.t. the traded amount. A characterisation of such functionals, together with their relationships\nwith arbitrages and other (more significant) market inefficiencies, is explored.
Loading....