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

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.

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Correspondence to Christoph Belak.

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Belak, C., Sass, J. Finite-horizon optimal investment with transaction costs: construction of the optimal strategies. Finance Stoch 23, 861–888 (2019). https://doi.org/10.1007/s00780-019-00404-4

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Keywords

  • Utility maximisation
  • Transaction costs
  • Reflected diffusions
  • Superharmonic functions

Mathematics Subject Classification (2010)

  • 93E20
  • 35R35
  • 91G80

JEL Classification

  • G11
  • C61