Acceptability indexes via \(g\)-expectations: an application to liquidity risk

Recently, several authors focused their attention on acceptability indexes (AI) and their applications in Finance. The AI notion turns out to be quite flexible and several applications in different directions have been proposed. In particular, in Cherny and Madan (Int J Theor Appl Finance 13(8):1149–1177, 2010) illiquid markets are modeled via AI and bid and ask prices are described through a “Conic Finance” approach. A different approach of dynamic type to bid and ask prices has been suggested by Bion-Nadal (J Math Econ 45(11):738–750, 2009), taking into account both transaction costs and liquidity risk, and based on time consistent pricing procedures. The purpose of the present paper is to suggest a further link between AI and risk measures based on the notion of \(g\)-expectation, and by this powerful tool to fill the gap between the static description of liquidity introduced by Corcuera et al. (Int J Portfolio Anal Manag 1(1):80–91, 2012) and the dynamic description provided by Bion-Nadal (J Math Econ 45(11):738–750, 2009).