Portfolio optimization in the presence of asset price bubbles

This paper studies portfolio optimization over terminal wealth in a finite horizon, arbitrage-free, competitive and frictionless market with a single risky asset and money market account, where the risky asset exhibits a price bubble. We show that in a complete market, the existence of a price bubble does not change an investor's welfare relative to an otherwise identical market with no bubble. The reason is that the optimal trading strategy enables the investor to avoid the losses due to a bubble and still obtain the risky asset's fundamental value. In an incomplete market, we provide a sufficient condition for the same conclusion to apply. This sufficient condition holds for a large class of Markov diffusion processes. An example is provided to show that bubbles can increase an investor's welfare if the sufficient condition is violated. We further show that, given certain trading constraints (e.g. collateral requirements), asset price bubbles can also decrease an investor's welfare.