Some remarks on functionally generated portfolios
Johannes Ruf*, UCL; Ioannis Karatzas, Columbia
In the first part of the talk I will review Bob Fernholz’ theory of functionally generated portfolios. In the second part I will discuss questions related to the existence of short-term arbitrage opportunities. This is joint work with Ioannis Karatzas
Martingale Optimal Transport and Beyond
Marcel Nutz*, Columbia
We study the Monge–Kantorovich transport between two probability measures, where the transport plans are subject to a probabilistic constraint. For instance, in the martingale optimal transport problem, the transports are laws of martingales. Interesting new couplings emerge as optimizers in such problems.
Constrained transport arises in the context of robust hedging in mathematical finance via linear programming duality. We formulate a complete duality theory for general performance functions, including the existence of optimal hedges. This duality leads to an analytic monotonicity principle which describes the geometry of optimal transports. Joint work with Mathias Beiglböck, Florian Stebegg and Nizar Touzi.
Dynamic Programming Approach to Principal-Agent Problems
Dylan Possamaï*, Université Paris Dauphine; Nizar Touzi, Ecole Polytechnique; Jaksa Cvitanic, Caltech
We consider a general formulation of the Principal-Agent problem with a lump-sum payment on a finite horizon. Our approach is the following: we first find the contract that is optimal among those for which the agent’s value process allows a dynamic programming representation and for which the agent’s optimal effort is straightforward to find. We then show that, under technical conditions, the optimization over the restricted family of contracts represents no loss of generality. Moreover, the principal’s problem can then be analyzed by the standard tools of control theory. Our proofs rely on the Backward Stochastic Differential Equations approach to non-Markovian stochastic control, and more specifically, on the recent extensions to the second order case.