Author(s)

Erio Castagnoli¹, Marzia De Donno², Gino Favero², Paola Modesti^2*

¹Accademia Nazionale Virgiliana and Università Bocconi, Mantova and Milan, Italy.
²Università degli Studi di Parma Dipartimento di Economia, Parma, Italy.

Linear price systems, typically used to model “perfect” markets, are widely known not to accommodate most of the typical frictions featured in “actual” ones. Since some years, “proportional” frictions (taxes, bid-ask spreads, and so on) are modeled by means of sublinear price functionals, which proved to give a more “realistic” description. In this paper, we want to introduce two more classes of functionals, not yet widely used in Mathematical Finance, which provide a further improvement and an even closer adherence to actual markets, namely the class of granular functionals, obtained when the unit prices of traded assets are increasing w.r.t. the traded amount; and the class of star-shaped functionals, obtained when the average unit prices of traded assets are increasing w.r.t. the traded amount. A characterisation of such functionals, together with their relationships with arbitrages and other (more significant) market inefficiencies, is explored.

Arbitrage, Asset Pricing, Super-Hedging, Granularity, Star-Shaped Prices

Castagnoli, E., De Donno, M., Favero, G., & Modesti, P. (2015) Granular and Star-Shaped Price Systems. Journal of Financial Risk Management, 4, 227-249. doi: 10.4236/jfrm.2015.43018.