Arbitrage and asset prices

We generalize the concept of utility arbitrage introduced in Page (Working Paper 401, Graduate School of Business, Indiana University, 1989) and provide a characterization. We also show that in an asset exchange economy with short selling and heterogeneous investors, an absence of unbounded utility arbitrages is necessary and sufficient for the existence of a general equilibrium. This result generalizes similar results by Hammond (Journal of Economic Theory, 1983, 31, 170-175) and Page (Working Paper 81/82-2-51, Department of Finance, University of Texas, 1982). Utility arbitrage occurs when investors can purchase utility-increasing portfolios for non-positive costs. In contrast, the standard condition of no arbitrage in finance dictates that there are no opportunities to purchase wealth-increasing portfolios for non-positive costs. In general, the absence of wealth-increasing arbitrage is not equivalent to the absence of unity-increasing arbitrage. To underscore the importance of this fact, we construct an example of a competitive asset exchange economy with complete markets and risk-averse investors in which there is an absence of wealth-increasing arbitrages, but there does not exist a competitive general equilibrium.