000K utf8 1100 $c2001 1500 ger 2050 urn:nbn:de:gbv:8-diss-4667 3000 Saß, Jörn 4000 Portfoliooptimierung unter Transaktionskosten$hChristian-Albrechts-Universität zu Kiel [Saß, Jörn] 4030 Kiel$nChristian-Albrechts-Universität zu Kiel 4209 Up to now numerous papers dealing with transaction costs were published in which transaction costs are defined in three different ways: Proportionally to volume of trade (proportional costs), proportionally to portfolio value (fixed costs) or consisting of a constant component and proportional costs (constant plus proportional costs). All approaches lead to plausible optimal strategies in view of the used transaction costs. But the results are not satisfieing in so far as either the transaction cost structure seems to be unrealistic or the optimal strategies are not practicable and hardly determinable. Our goal is to derive practicable optimal strategies for logarithmic utility. First, we analyze the CRR model in one period. We introduce a general cost structure containing the transaction cost models described above. Because of the simple structure, this model can be analyzed in a fairly complete way. In the CRR model with an infinite time-horizon we are able to embed our model in the theory of Markov controlled processes in discrete time. We solve some classical optimization problems without transaction costs and prove several existence results for the case that transaction costs are considered. Finally, we turn to the objective of maximizing the asymptotic growth rate in the continuous-time Black-Scholes model under fixed and proportional costs. We are able to prove a factorization of the wealth process. Using this and some renewal theory arguments we can reduce the problem in a suitable class of control strategies to a period between two trading times. If an optimal strategy exists in this class, it depends only on four parameters and can be determined in a numerically easy way. This result extends the results achieved by Morton and Pliska (1995) for fixed costs to combined fixed and proportional costs. The main difference is that we have to distinguish the new proportion of wealth after selling from the proportion of wealth after buying and hence the maximization has to be carried out over an initial distribution. 4950 https://nbn-resolving.org/urn:nbn:de:gbv:8-diss-4667$xR$3Volltext$534 4961 https://macau.uni-kiel.de/receive/diss_mods_00000466 5051 510 5550 Binomialmodell 5550 Black-Scholes model 5550 Black-Scholes-Modell 5550 CRR model 5550 fixed and proportional costs 5550 fixe und proportionale Kosten 5550 Portfoliooptimierung 5550 portfolio optimization 5550 Portfolio Selection 5550 Stochastisches Modell 5550 transaction costs 5550 Transaktionskosten 5550 Transaktionskostenansatz