We analyze conditional optimization problems arising in discrete-time dynamic Principal-Agent models of delegated portfolio management. In these models, an investor (the Principal) outsources her portfolio selection to a manager (the Agent) whose investment decisions the investor cannot or does not want to monitor. We prove that if both parties' preferences are time-consistent and translation invariant and under suitable assumptions on the class of admissible contracts the problem of dynamic contract design can be reduced to a series of one-period conditional optimization problems of risk-sharing type under constraints, that the first-best solution is implementable if it exists and that optimal contracts must generally make use of derivatives. We fully solve the dynamic contracting problem for a class of optimized certainty equivalent (OCE) utilities including expected exponential utilities and Average Value at Risk. If information is generated by finitely many random walks, then our conditional optimization problems reduce to standard optimization problems in Euclidean spaces. In this case derivatives are not part of optimal compensation schemes and the contracting problem can be solved for all OCE utilities. The talk is based on joint work with Julio Backhoff.
Financial Mathematics Seminar