Mathematical Finance and Probability Seminars (Since covid these events are taking place online.)

Shadow prices and well posedness in the problem of optimal investment and consumption with transaction costs

Tuesday, April 17, 2012 at 11:00am - 12:00pm

Speaker: Gordan Zitkovic, University of Texas at Austin

We revisit the optimal investment and consumption model of Davis and Norman (1990) and Shreve and Soner (1994), following a shadow-price approach similar to that of Kallsen and Muhle-Karbe (2010). Making use of the completeness of the model without transaction costs, we reformulate and reduce the Hamilton-Jacobi-Bellman equation for this singular stochastic control problem to a non-standard free-boundary problem for a first-order ODE with an integral constraint. Having shown that the free boundary problem has a smooth solution, we use it to construct the solution of the original optimal investment/consumption problem in a self-contained manner and without any recourse to the dynamic programming principle. Furthermore, we provide an explicit characterization of model parameters for which the value function is finite. This is joint work with Jinhyuk Choi and Mihai Sirbu.

Speaker: Gordan Zitkovic, University of Texas at Austin

Location   Hill 705