The martingale theory of bubbles studies the existence and characterization of asset price bubbles in continuous time and continuous trading economies under both the no arbitrage (no free lunch vanishing risk) and no dominance hypotheses. We review this theory, with an emphasis on understanding...

We survey several models of liquidity and liquidity related problems such as optimal execution of a large order, hedging and super-hedging options for a large trader, utility maximization in illiquid markets and price impact models with price manipulation strategies

Prices of financial options in a market with liquidity risk are shown to be weak solutions of a class of semilinear parabolic partial differential equations with nonnegative characteristic form. We prove the existence and uniqueness of such solutions, and then show the solutions correspond to...

We consider a setup in which a large trader has sold a number of American-style derivatives and can have an impact on prices by trading the underlying asset for hedging purposes. The price impacts are assumed to be temporary and decay exponentially with time. Due to the impact of trading on...