Utility Maximization with Constant Costs

We study the problem of maximizing expected utility of terminal wealth for an investor facing constant and proportional transaction costs in a multidimensional diffusion market. One of the main challenges is that the value... [ view full abstract ]

We study the problem of maximizing expected utility of terminal wealth for an investor facing constant and proportional transaction costs in a multidimensional diffusion market. One of the main challenges is that the value function turns out to be piecewise but not globally continuous. We establish this result via a combination of the stochastic Perron's method and a local comparison principle for viscosity solutions of nonlocal PDEs. We then use a characterization of the value function as the pointwise infimum of a suitable set of superharmonic functions to construct optimal trading strategies.