Stochastic measures of financial markets efficiency and integration

The notion of integration of different fmancial markets is often related to the absence of crossmarket arbitrage opportunities. Under the appropriated asswnptions and in absence of cross-market arbitrage opportunities, a riskneutral probability measure, shared by both markets, must exist. Some authors have considered this to provide some integration measures when the markets do not share any pricing rule, but always in static (or one period) asset pricing models. The purpose or this paper is to extend the refereed notions to a more general context. This is accomplished by introducing a methodology which may be applied in any intertemporal dynamic asset pricing model and without special asswnptions on the assets prices stochastic process. Then, the integration measures introduced here are stochastic processes testing different relative arbitrage profits and depending on the state of nature and on the date. The measures are introduced in a single fmancial market. When this market is not a global market from different ones, the measures simply test the degree of market efficiency. Transaction costs can be discounted in our model. Therefore, one can measure efficiency and integration in models with frictions. The main results are also interesting form a mathematical pint of view, since some topics of Operational Research are involved. We provide a procedure to solve a vector optimization problem with a non differentiable objective function and prove some properties about its sensitivity.