The Merton problem of optimizing the expected utility of consumption for a portfolio consisting of a bond and N stocks is considered when changes in the bond's interest rate, in the mean return rates and in the volatilities for the stock price processes are modelled by a finite-state Markov chain. This paper establishes an equivalent linear programming formulation of the problem. Two cases are considered. The first model assumes that these coefficients are known to the investor whereas the second model investigates a partially observed model in which the mean return rates and volatilities for the stocks are not directly observable.
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