Christoph Czichowsky

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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 which are not necessarily semimartingales, the existence of an(More)
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)
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)
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)
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)
The present paper accomplishes a major step towards a reconciliation of two conflicting approaches in mathematical finance: on the one hand, the mainstream approach based on the notion of no arbitrage (Black, Merton & Scholes); and on the other hand, the consideration of non-semimartingale price processes, the archetype of which being fractional Brownian(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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