This review is an introduction to asymptotic methods for portfolio choice problems with small transaction costs. We outline how to derive the corresponding dynamic programming equations and how to simplify them in the small-cost limit. This allows one to obtain explicit solutions in a wide range...

In this survey, we show that various stochastic optimization problems arising in option theory, in dynamical allocation problems, and in the microeconomic theory of intertemporal consumption choice can all be reduced to the same problem of representing a given stochastic process in terms of...

We analyze numerically the superreplication problem and the associatedhedging strategy in an illiquid binomial market. We prove theexistence of an optimal feedback strategy for European and barrier optionsand compute it numerically by means of a dynamic programmingprinciple. We exhibit that the...