Essays on finance and agency theory

This dissertation studies financial decision-making in situations when financial markets are predictable. It contains three contributions: (1) It applies the min-max method of robust control to the handling of risk of persistent mispricing in arbitrage situations. (2) It shows how an investor can use agency schemes to elicit truthful predictions from experts who can communicate with each other. (3) It develops a method for finding optimal leverage policy in situations of convergent trading.; After an introduction, the second chapter assumes that existing mispricing between the derivative and the underlying asset can persist and that the investor is constrained in his ability to sell the underlying asset short. A temporary increase in mispricing can produce losses and limit the investor's potential for future gains. I study how the investor can use the minmax method of robust control to guarantee a positive profit and apply this method to an example. I derive both the optimal investment policy and bounds on the amount of guaranteed profit.; The third chapter studies a situation in which a client has to extract information from lazy communicating experts. I find that: (1) It is impossible to induce the experts to do research and report the results truthfully if payments to them depend only on their own predictions. (2) It is possible to do this if the payments can depend as well on the other experts' predictions. (3) The scheme that implements this information extraction brings additional costs to the client, but only if the experts are risk averse. (4) The experts can be worse off under these schemes.; The fourth chapter examines investment in a mispriced asset when the date the price will converge to its theoretically correct value is uncertain. I study the optimal leverage policy of the investor who cares only about the long-run distribution of his wealth. I find that the optimal differentiable policy is linear in the amount of mispricing, and that the optimal threshold policy has coinciding thresholds. I derive expressions for the investor's objective function under these rules and apply the results to an empirical example.