Winslow Strong (PSTAT, UCSB)

Title: Regulation and the Removal of Arbitrage in Strongly Markovian Equity Market Models

Abstract: Recent studies of stochastic models of equity markets have raised new and surprising questions with respect to the importance and realism of the assumption of no arbitrage. E. R. Fernholz has pointed out that we both observe in the data and expect on theoretical grounds that equity markets are diverse in the sense that no single company's capitalization can approach the capitalization of the whole market. The implication of this is that modulo some mild technical conditions in any model where stocks are diffusion processes (and therefore continuous) that any passive (buy-and-hold) portfolio can be outperformed with probability 1 over a prespecified sufficiently long time horizon. In the real world this translates into the existence of portfolios which are statistical arbitrages with respect to the market portfolio. In this talk we lift the assumption of continuity in a very mild way by imposing a form of regulation in the market model whereby market portfolio weights are confined within a region of our choosing by reallocation of money amongst companies upon exit from this region. This allows us to create regulated versions of certain strongly Markovian market models which may have admitted arbitrage in unregulated form but are both diverse and free of arbitrage in their regulated form. We discuss many of the particular models which admit arbitrage and whether or not this procedure is applicable to those models.