Optimization in a Frictionless Market
Steven E. Shreve, Carnegie Mellon University, United States
Date:
09 Sep 2014
Time:
10.00am – 12.00pm
Venue:
I3 Building, Executive Seminar Room Level 4
(This interdisciplinary PhD Lecture is organized jointly with the Risk Management Institute and NUS Finance & Risk Management Cluster)
About the Speaker
Steven Shreve is the Orion Hoch University Professor of Mathematics at Carnegie Mellon University, where he co-founded Carnegie Mellon’s Master’s degree in Computational Finance, now in its 20th year, with campuses in New York and Pittsburgh. Shreve received an MS in electrical engineering and a PhD in mathematics from the University of Illinois. Shreve has also been a faculty member of the University of California at Berkeley and Massachusetts Institute of Technology. Shreve’s book “Stochastic Calculus for Finance” won the 2004 Wilmott award for “Best New Book in Quantitative Finance.” Shreve is co-author of the books “Brownian Motion and Stochastic Calculus” and “Methods of Mathematical Finance,” advisory editor of the journal “Finance and Stochastics,” and past-President of the Bachelier Finance Society. He has published over forty articles in scientific journals on stochastic calculus, stochastic control, and the application of these subjects to finance, including the effect of transaction costs on option pricing, the effect of unknown volatility on option prices, pricing and hedging of exotic options, and models of credit risk.
Abstract
This is the first in a pair of lectures and lays the groundwork for the second lecture, which deals with portfolio optimization in the presence of proportional transaction costs. In this lecture, we take the well-studied example of optimal investment and consumption on an infinite horizon and solve it both by solving the Hamilton-Jacobi-Bellman equation and by the martingale method. In addition, we introduce the notion of viscosity solutions of the Hamilton-Jacobi-Bellman equation.
