Equilibrium Asset Returns in Financial Markets

Return distributions in the class of pure jump limit laws are observed to reflect numerous asymmetries between the upward and downward motions of asset prices. The return distributions are modeled by self decomposable parametric laws with all parameters continuously responding to each other. Fixed points of the response functions define equilibrium distributions. The equilibrium distributions that can arise in practice are constrained by the level of return acceptability they may attain. As a consequence expected returns are the cost of purchasing the the negative of the centered return. They are then equal to the ask price in two price economies, for the centered and negated return. The asymmetries studied include differences in scale, speed, power variation, excitation and cross excitation