his 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 A of admissible strategies is restricted. The classical notion of martingale is replaced with the notion of A-martingale. A calculus related to 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.
Coviello R., DI GIROLAMI, C., Russo F. (2011). On stochastic calculus related to financial assets without semimartingales. BULLETIN DES SCIENCES MATHEMATIQUES, 135(6-7), 733-774 [10.1016/j.bulsci.2011.06.008].
On stochastic calculus related to financial assets without semimartingales
DI GIROLAMI, Cristina;
2011
Abstract
his 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 A of admissible strategies is restricted. The classical notion of martingale is replaced with the notion of A-martingale. A calculus related to 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
