Optimal Consumption and Investment for Exponential Utility Function
We investigate an optimal consumption and investment problem for Black-Scholes type financial market
on the whole investment interval [0, T]. We formulate various utility maximization problem, which can
be solved explicitly. The method of solution uses the convex dual function (Legendre transform) of the
utility function. Related to this concept, we introduce and study the convex dual of the value function for
our problem.
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