Optimal investment with 'random endowment' is an important topic because of the connection with asset valuation and hedging of liabilities in incomplete markets. In this talk we revisit Merton's classic problem of maximizing utility of consumption over an infinite time horizon when asset prices are log-normal. Merton already noted how to adapt the solution to accommodate a known income stream, and a similar argument applies to any hedgeable income stream. When the income is not hedgeable the situation is much more complicated. We study a specific problem by duality methods. The dual minimization problem is one of deterministic optimal control, for which we obtain a computable solution.
This is joint work with Michel Vellekoop.
On Mark Davis' website there are slides of this talk available.