Kiel

We reconsider Merton's problem under proportional transaction costs.

Beginning with Davis and Norman (1990) such utility maximization problems are usually solved using stochastic control theory.

Martingale methods, on the other hand, have so far only been used to derive general structural results. These apply the duality theory for frictionless markets typically to a fictitious shadow price process lying within the bid-ask bounds of the real price process.

In this study we show that this dual approach can actually be used for both deriving a candidate solution and verification.

In particular, the shadow price process is determined explicitly.