POWER UTILITY MAXIMIZATION IN CONSTRAINED EXPONENTIAL LÉVY MODELS

Marcel Nutz

35 citations0/0 files storedMathematical Finance

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Stochastic processes and financial applications Risk and Portfolio Optimization Probability and Risk Models

Abstract

We study power utility maximization for exponential Lévy models with portfolio constraints, where utility is obtained from consumption and/or terminal wealth. For convex constraints, an explicit solution in terms of the Lévy triplet is constructed under minimal assumptions by solving the Bellman equation. We use a novel transformation of the model to avoid technical conditions. The consequences for q‐optimal martingale measures are discussed as well as extensions to nonconvex constraints.

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References

1969Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case 1981Martingales and stochastic integrals in the theory of continuous trading 2003Limit Theorems for Stochastic Processes 1969Lifetime Portfolio Selection By Dynamic Stochastic Programming 1999The asymptotic elasticity of utility functions and optimal investment in incomplete markets 2003Lévy Processes in Finance 1968Optimal Multiperiod Portfolio Policies 2007The numéraire portfolio in semimartingale financial models

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