In continuous-time stochastic calculus a limit in probability is used to extend the definition of the stochastic integral to the case where the integrand is not square-integrable at the endpoint of the time interval under consideration. When the extension is applied to portfolio strategies,...

The paper generalizes and refines the Fundamental Theorem of Asset Pricing of Dalang, Morton and Willinger in the following two respects: (a) the result is extended to a model with portfolio constraints; (b) versions of the no-arbitrage criterion based on the bang-bang principle in control...