In a financial market with a continuous price process and proportional transaction costs we investigate the problem of utility maximization of terminal wealth. We give sufficient conditions for the existence of a shadow price process, i.e.~a least favorable frictionless market leading to the...

For portfolio choice problems with proportional transaction costs, we discuss whether or not there exists a shadow price, i.e., a least favorable frictionless market extension leading to the same optimal strategy and utility. By means of an explicit counter-example, we show that shadow prices...

For portfolio choice problems with proportional transaction costs, we discuss whether or not there exists a "shadow price", i.e., a least favorable frictionless market extension leading to the same optimal strategy and utility. By means of an explicit counter-example, we show that shadow prices...

For portfolio optimisation under proportional transaction costs, we provide a duality theory for general cadlag price processes. In this setting, we prove the existence of a dual optimiser as well as a shadow price process in a generalised sense. This shadow price is defined via a "sandwiched"...

While absence of arbitrage in frictionless financial markets requires price processes to be semimartingales, non-semimartingales can be used to model prices in an arbitrage-free way, if proportional transaction costs are taken into account. In this paper, we show, for a class of price processes...

Let S be an Rd-valued semimartingale and ( n) a sequence of C-valued inte-grands, i.e., predictable, S-integrable processes taking values in some given closedset C(!, t) ⊆ Rd which may depend on the state ! and time t in a predictable way.Suppose that the stochastic integrals ( n · S)...

Consider an Rd-valued semimartingale S and a sequence of Rd-valuedS-integrable predictable processes Hn valued in some closed convex set K C Rd,containing the origin. Suppose that the real-valued sequence Hn * S converges toX in the semimartingale topology.[...]

The Markowitz problem consists of finding in a financial market a self-financingtrading strategy whose final wealth has maximal mean and minimal variance. Westudy this in continuous time in a general semimartingale model and under coneconstraints: Trading strategies must take values in a...