Portfolio and consumption choice with habit formation under inflation

We investigate the optimal portfolio and consumption policies for a finite-horizon investor in a life-cycle model with habit formation and inflation risk. We consider two types of habit investors: one forms habit based on real past consumption, while the other on nominal past consumption, which is motivated by money illusion. The optimal strategy is expressed explicitly in terms of the solution toa linear partial differential equation. We find that the effects of inflation on the optimal strategy depend on the type of habit investor, because it determines the risk profile of the hedge portfolio and subsistence portfolio. This dependence isrobust to the incompleteness of the financial market.