An Explicit Example Of Optimal Portfolio-Consumption Choices With Habit Formation And Partial Observations
Abstract
We consider a model of optimal investment and consumption with both habit formation and partial observations in incomplete It\^{o} processes market. The investor chooses his consumption under the addictive habits constraint while only observing the market stock prices but not the instantaneous rate of return. Applying the Kalman-Bucy filtering theorem and the Dynamic Programming arguments, we solve the associated Hamilton-Jacobi-Bellman (HJB) equation explicitly for the path dependent stochastic control problem in the case of power utilities. We provide the optimal investment and consumption policies in explicit feedback forms using rigorous verification arguments.
Keywords
Cite
@article{arxiv.1112.2939,
title = {An Explicit Example Of Optimal Portfolio-Consumption Choices With Habit Formation And Partial Observations},
author = {Xiang Yu},
journal= {arXiv preprint arXiv:1112.2939},
year = {2014}
}
Comments
Key words: Consumption habit formation, Kalman-Bucy filtering, Path-dependent stochastic control, Verification theorem