Brennan 1998: The Role of Learning in Dynamic Portfolio Decisions

2 assets: bond and stock

1. bond gives constant rate of return
2. stock price:

wealth process:

here is fraction of wealth in risky asset

Investor unable to observe . At , investor views the distro of as .

We denote the conditional expectation and variance of by . By Lipster-Shiryayev 1978 (see Gennotte 1986 for a simple exposition), we have:

2. (deterministic dynamics)

investor’s value function at depends on current wealth, current assessment of , and . Denote it as .

formulate HJB, then use ansatz , and derive an HJB for .