学术讲座

12月12日下午14：00

地点：数计学院3号楼107

Portfolio optimization: the Dual Optimizer and Stability

Lingqi Gu

Fakultat fur Mathematik, Universitat Wien, Austria

Abstract

We consider the dual problem of portfolio optimization problems in markets with/without

transaction costs, especially the property of optimal dual processes which produce the unique

dual optimizer (solution) to the dual problem.

Even in an incomplete semimartingale market, in general, the unique optimal dual process

is not a local martingale but a supermartingale. However, if the stock price is a continuous

semimartingale, then the optimal dual process is a local martingale. This result can be

extended to the case with bounded random endowment. Precisely, the countable additive

part of the dual optimizer obtained by Cvitani_c, Schachermayer, Wang in 2001 can be attained

by a local martingale bY , which is a supermartingale deator de_ned by Kramkov and

Schachermayer in 1999, when the underlying _ltration is generated by Brownian motion.

Then we discuss such problem in markets with transaction costs, where the stock price

process is continuous. Under suffcient conditions, all optimal dual processes (may not be

unique) are local martingales. Then, we consider the convergence of optimal dual processes

and shadow price processes, after having acquired static stability of the utility maximization

problem.