The method of variational inequalities is a useful theoretical tool in stochastic control, but there are few problems in which this method leads to an explicit solution. We present such a problem drawn from portfolio management. An agent can distribute his wealth between two investments, one...

We consider optimal consumption and portfolio investment problems of an investor who is interested in maximizing his utilities from consumption and terminal wealth subject to a random inflation in the consumption basket price over time. We consider two cases: (i) when the investor observes the...