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Optimal consumption and Investment with Lévy Processes for power utility functions



We consider an optimal investment and consumption problem in continuous time for incomplete markets model when the security prices follow a Geometric Lévy process with deterministic coefficients on the whole investment interval [0; T]: Using the conditions for the existence of optimal portfolio policies to construct the state price density and for the set of all equivalent martingale measure EMM, we introduce and study the convex dual function (Legendre transform) of the power utility. Related to this concept, we formulate and solve our problem.


Portfolio optimization, Incomplete markets model, Lévy processes, power utility, consumption.

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