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Finite-horizon optimal investment with transaction costs: construction of the optimal strategies

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  • Christoph Belak

    (Technische Universität Berlin)

  • Jörn Sass

    (University of Kaiserslautern)

Abstract

We revisit the problem of maximising expected utility of terminal wealth in a Black–Scholes market with proportional transaction costs. While it is known that the value function of this problem is the unique viscosity solution of the HJB equation and that the HJB equation admits a classical solution on a reduced state space, it has been an open problem to verify that these two coincide. We establish this result by devising a verification procedure based on superharmonic functions. In the process, we construct optimal strategies and provide a detailed analysis of the regularity of the value function.

Suggested Citation

  • Christoph Belak & Jörn Sass, 2019. "Finite-horizon optimal investment with transaction costs: construction of the optimal strategies," Finance and Stochastics, Springer, vol. 23(4), pages 861-888, October.
    • Handle: RePEc:spr:finsto:v:23:y:2019:i:4:d:10.1007_s00780-019-00404-4
    DOI: 10.1007/s00780-019-00404-4
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    References listed on IDEAS

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    Cited by:

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    More about this item

    Keywords

    Utility maximisation; Transaction costs; Reflected diffusions; Superharmonic functions;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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