The study of evolutionary dynamics was so far mainly restricted to finite strategy spaces. In this paper we show that this unsatisfying restriction is unnecessary. We specify a simple condition under which the continuous time replicator dynamics are well defined for the case of infinte strategy...

In the framework of the classical Black and Scholes model of security market we present the explicit formulas of the minimal hedging portfolios for a number of reward processes of the ``classical'', lookback and Asian type. These results complement the solutions previously received by Mc~Kean,...

We develop a new approach to pricing and hedging contingent claims in incomplete markets. Mimicking as closely as possible in an incomplete markets framework the no--arbitrage arguments that have been developed in complete markets leads us to defining the concept of pseudo--arbitrage. Building...

Let M(X) be a family of all equivalent local martingale measures for some locally bounded d-dimensional process X, and V be a positive process. Main result of the paper (Theorem 2.1) states that the process V is a supermartingale whatever Q in M(X), if and only if this process admits the...

The evolutionary selection of outcomes (modelled using the replicator dynamics) in games with costless communication depends crucially on the structural assumptions made on the underlying population. (1) In conflicts between two interacting populations, common interest implies that the set of...

The effect that exogenous mistakes, made by players choosing their strategies, have on the dynamic stability for the replicator dynamic is analyzed for both asymmetric and symmetric normal form games. Through these perturbed games, the dynamic solution concept of limit asymptotic stability is...

The analysis of the replicator dynamic in generic perfect information games yields the following results. In the long run, players play a Nash equilibrium provided that initially all strategies are present. There is at most one ``stable'' component (formally, an interior asymptotically stable...