Asset price bubbles, wealth preserving, dominating, and replicating trading strategies

This paper studies an arbitrage-free, competitive and frictionless market with trading in a single risky asset and money market account, where the risky asset exhibits a price bubble. We analyze two sets of self-financing and admissible trading strategies in this market. The first are simple trading strategies, and the second are trading strategies that replicate or super-replicate the risky asset's payoffs at the model's horizon. We show that in both sets there exist wealth preserving trading strategies, i.e. trading strategies whose initial value equals the present value of its future cash flows. And, in the second set, we show that there are wealth preserving replicating trading strategies that dominate buying and holding the risky asset. The practical applications of these insights are discussed.