主 题: Finite Horizon Optimal Investment and Consumption with Proportional Transaction Costs
报告人: 戴民 教授 (National University of Singapore)
时 间: 2008-12-19 下午 2:00 - 3:00
地 点: 理科一号楼 1114(数学所活动)
We are concerned with the finite horizon optimal investment and
consumption with proportional transaction costs. This is a
singular stochastic control problem and the associated value
function is governed by a parabolic variational inequality with
gradient constraints which gives rise to two time-dependent free
boundaries. The free boundaries correspond to the optimal buying
and selling strategies. Relying on a partial differential equation
approach, we prove that the problem can be reduced to a standard
variational inequality through which the behaviors of the free
boundaries can be completely characterized. Our result essentially
indicates a connection between singular control and optimal
stopping, which has never been revealed for the present problem.
The regularity of value function and the smoothness of free
boundaries are also proved.
