Faculty in Mathematical Finance
Math Finance Home
Conferences
Seminars
People
Open Positions
Contact |
CCF Seminar
Sergey Nadtochiy University of Michigan Title: Optimal contract for fund manager, with capital injections and endogenous trading constraints Abstract: In this paper, we construct a solution to the optimal contract problem for delegated portfolio management of the fist-best (risk-sharing) type. The novelty of our result is (i) in the robustness of the optimal contract with respect to perturbations of the wealth process (interpreted as capital injections), and (ii) in the more general form of principalâ€™s objective function, which is allowed to depend directly on the agentâ€™s strategy, as opposed to being a function of the generated wealth only. In particular, the latter feature allows us to incorporate endogenous trading constraints in the contract. We reduce the optimal contract problem to the following inverse problem: for a given portfolio (defined in a feedback form, as a random field), construct a stochastic utility whose optimal portfolio coincides with the given one. We characterize the solution to this problem through a Stochastic Partial Differential Equation (SPDE), prove its well-posedness, and compute the solution explicitly in the Black-Scholes model. (Joint work with Thaleia Zariphopoulou.) Date: Monday, April 30, 2018 Time: 4:30 pm Location: Wean Hall 8220 Submitted by: Johannes Muhle-Karbe |