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CRRA Utility Maximization Over a Finite Horizon in an Exponential Levy Model with Finite Activity

Author

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  • Baccarin Stefano

    (Department of Economics, Social Studies, Applied Mathematics and Statistics, University of Torino, Torino, Italy;)

Abstract

We study a dynamic portfolio optimization problem over a finite horizon with n risky securities and a risk-free asset. The prices of the risky securities are modelled by ordinary exponentials of jump- diffusions. The goal is to maximize the expected discounted utility from both consumption up to the final horizon and terminal wealth. We prove a verification theorem that characterize the value function and the optimal policy by means of a regular solution of a HJB partial integro-differential equation. The verification theorem is used to obtain closed-form expressions for the value function and the optimal policy considering power and logarithmic utility functions.

Suggested Citation

  • Baccarin Stefano, 2024. "CRRA Utility Maximization Over a Finite Horizon in an Exponential Levy Model with Finite Activity," Working papers 092, Department of Economics, Social Studies, Applied Mathematics and Statistics (Dipartimento di Scienze Economico-Sociali e Matematico-Statistiche), University of Torino.
    • Handle: RePEc:tur:wpapnw:092
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    File URL: https://www.bemservizi.unito.it/repec/tur/wpapnw/m92.pdf
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    References listed on IDEAS

    as
    1. Kristin Reikvam & Fred Espen Benth & Kenneth Hvistendahl Karlsen, 2001. "Optimal portfolio selection with consumption and nonlinear integro-differential equations with gradient constraint: A viscosity solution approach," Finance and Stochastics, Springer, vol. 5(3), pages 275-303.
    2. Framstad, Nils Chr. & Oksendal, Bernt & Sulem, Agnes, 2001. "Optimal consumption and portfolio in a jump diffusion market with proportional transaction costs," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 233-257, April.
    3. Kristin Reikvam & Fred Espen Benth & Kenneth Hvistendahl Karlsen, 2001. "Optimal portfolio management rules in a non-Gaussian market with durability and intertemporal substitution," Finance and Stochastics, Springer, vol. 5(4), pages 447-467.
    4. Dimitri Vallière & Yuri Kabanov & Emmanuel Lépinette, 2016. "Consumption-investment problem with transaction costs for Lévy-driven price processes," Finance and Stochastics, Springer, vol. 20(3), pages 705-740, July.
    5. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Optimal consumption/investment over a finite horizon; CRRA utility; Dynamic programming; Levy processes with finite activity; Integro-differential PDE;
    All these keywords.

    JEL classification:

    • H7 - Public Economics - - State and Local Government; Intergovernmental Relations
    • H70 - Public Economics - - State and Local Government; Intergovernmental Relations - - - General
    • H77 - Public Economics - - State and Local Government; Intergovernmental Relations - - - Intergovernmental Relations; Federalism
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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