Stochastic Finance, 4th Edition

3Optimality and equilibrium

Consider an investor whose preferences can be expressed in terms of expected utility. In Section 3.1, we discuss the problem of constructing a portfolio which maximizes the expected utility of the resulting payoff. The existence of an optimal solution is equivalent to the absence of arbitrage opportunities. This leads to an alternative proof of the “fundamental theorem of asset pricing”, and to a specific choice of an equivalent martingale measure defined in terms of marginal utility. Section 3.2 contains a detailed case study describing the interplay between exponential utility and relative entropy. In Section 3.3, the optimization problem is formulated for general contingent claims. Typically, optimal profiles will ...