Castagnoli, E., Favero, G., & Modesti, P. (in print). Price Systems for Random Amounts: A Unified Approach. In D. Jakóbczak (Ed.), Analyzing Risk through Probabilistic Modeling in Operations Research. Hershey: IGI Global.

has been cited by the following article:

• TITLE: Granular and Star-Shaped Price Systems

  AUTHORS: Erio Castagnoli, Marzia De Donno, Gino Favero, Paola Modesti

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

  JOURNAL NAME: Journal of Financial Risk Management, Vol.4 No.3, September 30, 2015

  ABSTRACT: 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.