2017/03/03 by Frittelli, Marco, Maggis, Marco
#FOS: Economics and business #Mathematical Finance (q-fin.MF) #Risk Management (q-fin.RM)
paper · doi:10.48550/arxiv.1703.01329
We propose a method to assess the intrinsic risk carried by a financial position X when the agent faces uncertainty about the pricing rule assigning its present value. Our approach is inspired by a new interpretation of the quasiconvex duality in a Knightian setting, where a family of probability measures replaces the single reference probability and is then applied to value financial positions. Diametrically, our construction of Value&Risk measures is based on the selection of a basket of claims to test the reliability of models. We compare a random payoff X with a given class of derivatives written on X , and use these derivatives to \textquotedblleft test\textquotedblright the pricing measures. We further introduce and study a general class of Value&Risk measures % R(p,X,ℙ) that describes the additional capital that is required to make X acceptable under a probability ℙ and given the initial price p paid to acquire X.