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Optimal Portfolios and Pricing of Financial Derivatives Under Proportional Transaction Costs

In: Markov Decision Processes in Practice

Author

Listed:
  • Jörn Sass

    (TU Kaiserslautern)

  • Manfred Schäl

    (Universität Bonn)

Abstract

A utility optimization problem is studied in discrete time 0 ≤ n ≤ N for a financial market with two assets, bond and stock. These two assets can be traded under transaction costs. A portfolio (Y n , Z n ) at time n is described by the values Y n and Z n of the stock account and the bank account, respectively. The choice of (Y n , Z n ) is controlled by a policy. Under concavity and homogeneity assumptions on the utility function U, the optimal policy has a simple cone structure. The final portfolio (Y N ∗, Z N ∗) under the optimal policy has an important property. It can be used for the construction of a consistent price system for the underlying financial market.

Suggested Citation

  • Jörn Sass & Manfred Schäl, 2017. "Optimal Portfolios and Pricing of Financial Derivatives Under Proportional Transaction Costs," International Series in Operations Research & Management Science, in: Richard J. Boucherie & Nico M. van Dijk (ed.), Markov Decision Processes in Practice, chapter 0, pages 523-546, Springer.
    • Handle: RePEc:spr:isochp:978-3-319-47766-4_21
    DOI: 10.1007/978-3-319-47766-4_21
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