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Optimal investment and consumption for financial markets with jumps under transaction costs

Author

Listed:
  • Sergei Egorov

    (Normandie Univ, LMRS UMR 6085
    National Research Tomsk State University)

  • Serguei Pergamenchtchikov

    (Normandie Univ, LMRS UMR 6085)

Abstract

We consider a portfolio optimisation problem for financial markets described by semimartingales with independent increments and jumps defined through Lévy processes. First, for power utility functions, we show a corresponding verification theorem and then find optimal consumption/investment strategies in an explicit form. Moreover, on the basis of the strategies constructed using the Leland–Lépinette approach, we develop an asymptotic optimal investment and consumption method for financial markets with proportional transaction costs when the number of portfolio revisions tends to infinity. Finally, we provide Monte Carlo simulations to numerically illustrate the obtained results in practice.

Suggested Citation

  • Sergei Egorov & Serguei Pergamenchtchikov, 2024. "Optimal investment and consumption for financial markets with jumps under transaction costs," Finance and Stochastics, Springer, vol. 28(1), pages 123-159, January.
    • Handle: RePEc:spr:finsto:v:28:y:2024:i:1:d:10.1007_s00780-023-00521-1
    DOI: 10.1007/s00780-023-00521-1
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    References listed on IDEAS

    as
    1. Leland, Hayne E, 1985. "Option Pricing and Replication with Transactions Costs," Journal of Finance, American Finance Association, vol. 40(5), pages 1283-1301, December.
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    9. Belkacem Berdjane & Serguei Pergamenshchikov, 2013. "Optimal consumption and investment for markets with random coefficients," Finance and Stochastics, Springer, vol. 17(2), pages 419-446, April.
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    More about this item

    Keywords

    Financial markets; Optimal investment/consumption problem; Stochastic control; Dynamic programming; Hamilton–Jacobi–Bellman equation;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G23 - Financial Economics - - Financial Institutions and Services - - - Non-bank Financial Institutions; Financial Instruments; Institutional Investors

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