Optimal Portfolios and Pricing of Financial Derivatives Under Proportional Transaction Costs

Jörn Sass () and Manfred Schäl ()
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Jörn Sass: TU Kaiserslautern
Manfred Schäl: Universität Bonn

Chapter Chapter 21 in Markov Decision Processes in Practice, 2017, pp 523-546 from Springer

Abstract: 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.

Keywords: Numeraire portfolio; Utility function; Consistent price system; Proportional transaction costs; Dynamic programming (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:isochp:978-3-319-47766-4_21

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DOI: 10.1007/978-3-319-47766-4_21

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