Goran Peskir
Nonlinear Optimal Stopping and Nonlinear Optimal Control
I will discuss problems of (a) optimal stopping and (b) optimal stochastic control in which the performance criteria are expressed by means of nonlinear functionals of the expected values. This leads to spatial/temporal inconsistencies which require novel concepts of solution. The three solution concepts known presently can be classified in terms of commitment to (i) the past (time-inconsistent), (ii) the future (Strotz subgame-perfect Nash equilibrium), (iii) the present
(dynamic optimality). Discussion will be illustrated through optimal mean-variance portfolio selection problems. This will include a description of the first known time-consistent solutions to the constrained versions of these problems in continuous time (dating back to Markowitz in 1952 for a single period model).