On stochastic calculus related to financial assets without   semimartingales
  This paper does not suppose a priori that the evolution of the price of a financial asset is a semimartingale. Since possible strategies of investors are self-financing, previous prices are forced to be finite quadratic variation processes. The non-arbitrage property is not excluded if the class $\mathcal{A}$ of admissible strategies is restricted. The classical notion of martingale is replaced with the notion of $\mathcal{A}$-martingale. A calculus related to $\mathcal{A}$-martingales with some examples is developed. Some applications to no-arbitrage, viability, hedging and the maximization of the utility of an insider are expanded. We finally revisit some no arbitrage conditions of Bender-Sottinen-Valkeila type. 
Rosanna Coviello (LAGA), Cristina Di Girolami (ENSTA ParisTech, Luiss   Guido Carli), Francesco Russo (ENSTA ParisTech, INRI...
math.PR q-fin.PR