Seminar Event Detail

Financial/Actuarial Mathematics

Date:  Wednesday, April 04, 2018
Location:  4096 East Hall (3:00 PM to 4:00 PM)

Title:  Optimal Contract for a Fund Manager, with Capital Injections and Endogenous Constraints.

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 principal’s
objective function, which is allowed to depend directly on the agent’s strategy (which, in
turn, allows us to incorporate endogenous 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 linear
Stochastic Partial Differential Equation (SPDE), prove its well-posedness, and compute the
solution explicitly in the Black-Scholes model. Remarkably, the optimal contract computed
in the Black-Scholes model satisfies the limited liability condition and has additional properties which show that it also solves the second-best (moral hazard) version of the problem, in
which the principal cannot fully deduce the agent’s strategy from her observations.


Speaker:  Sergey Nadtochiy

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