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- Christoph Czichowsky
- Finance and Stochastics
- 2013

In this thesis we study the utility maximization problem for power utility random elds in a general semimartingale nancial market, with and without intermediate consumption. The notion of an opportunity process is introduced as a reduced form of the value process for the resulting stochastic control problem. This process is shown to describe the key… (More)

- Christoph Czichowsky, Johannes Muhle-Karbe, Walter Schachermayer
- SIAM J. Financial Math.
- 2014

Given a sequence (M n) ∞ n=1 of non-negative martingales starting at M n 0 = 1 we find a sequence of convex combinations (M n) ∞ n=1 and a limiting process X such that (M n τ) ∞ n=1 converges in probability to X τ , for all finite stopping times τ. The limiting process X then is an optional strong supermartingale. A counterexample reveals that the… (More)

For portfolio optimisation under proportional transaction costs, we provide a dual-ity theory for general c`adì ag 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 " process consisting of a predictable and an optional strong… (More)

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 same optimal strategy and utility as in the original market under… (More)

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 counterexample , we show that shadow prices may fail to exist even in seemingly perfectly benign situations,… (More)

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