Grenzen der Arbitrage (English shop)

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The publication is based on the model described by the authors Andrei Shleifer and Robert W. Vishny in their paper “The Limits of Arbitrage”, which builds on capital market imperfections. By considering different groups of market participants (investors, noise traders and arbitrageurs), each with different levels of information, the model belongs to the so-called “behavioral finance” models and can be assigned to behavioral economics, a modern subfield of economics.

Based on the template provided by Shleifer/Vishny, a complete decision model is developed. The input parameters and the specifications of the model are presented in detail and from an economic perspective. All restrictions on the input parameters are critically examined and the necessary restrictions are derived in detail. Imprecise or even erroneous passages, for example in connection with the optimal decision, are specified or corrected. In particular, fully exploiting the arbitrage opportunity in the situations indicated by the two authors is not always optimal. This can be shown especially by means of a state-based approach as well as an exact representation of the price in the first state of the second point in time. It can furthermore be demonstrated that at least one optimal solution always exists and that the optimal solution is unique in most cases. At most two optimal solutions can occur. Concrete numerical examples with accompanying figures illustrate the results. The investors’ update function is analysed in detail. In this context, non-linear update functions and their influence on the optimal decision are also examined. Dominance relations are used to distinguish the different update functions from one another. The assumption of full investment at the second point in time, when a further (stronger) “noise trader shock” occurs, leads to a suboptimal solution for some admissible parameter constellations. By extending the model with an additional decision variable, an improvement of the solution can be achieved in these cases. Within the framework of the decision model, an equally strong or a weaker noise trader shock at the second point in time is also taken into account, and the functioning of the model is ensured for those cases in which a complete withdrawal of funds occurs.