Application of Stochastic Flows to Optimal Portfolio Strategies

The author proposes a new algorithm using a stochastic flow technique to solve an optimal portfolio and consumption problem for a single-agent in a Markovian security market setting.In that class, optimal feedback portfolio strategies are computed by the system of stochastic differential equations, which are induced by applying the differential rule of a composite function to stochastic flows. Sufficient conditions for the existence of feedback solutions are stated using integrability of stochastic processes. In the case of power and logarithmic utility functions, more straightforward conditions are given and the continuity of optimal strategies is proved