Speaker: Nicole Bäuerle
Title: Competitive Portfolio Optimization
Abstract: Within a common arbitrage-free semimartingale financial market we consider the problem of determining all Nash equilibrium investment strategies for n agents who try to maximize the expected utility of their relative wealth. The utility function can be rather general here. Exploiting the linearity of the stochastic integral and making use of the classical pricing theory we are able to express all Nash equilibrium investment strategies in terms of the optimal strategies for the classical one agent expected utility problems. We give applications to specific financial markets and compare our results with those given in the literature. A more specific model with price impacts is also discussed. Moreover, we consider the problem of determining all Nash equilibrium investment strategies for n agents who try to maximize the expected utility of their wealth under the constraint that with certain probability the own wealth exceeds a linear combination of the others. We compare the investment strategy to the optimal one without competition. (Joint work with T. Göll)