Abstract
The wealth-consumption ratio of an investor, say, H must be calculated to solve models of optimal portfolios and asset prices. At this time there is no standard method to obtain H for investors with stochastic differential utility in incomplete markets. One reason is that boundary conditions of the Hamilton-Jacobi-Bellman equation are unkown. I show that H solves a Feynman-Kac equation, which is a probabilistic representation of the HJB in which regularity conditions substitute for boundary conditions. FK equations are given for three settings: an exchange economy, a production economy, and a model of optimal portfolio choice. Explicit solutions for H are shown in two special cases of the exchange economy, and a numerical procedure to calculate H is provided for general cases.
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