Optimal Portfolios and Pricing of Financial Derivatives Under Proportional Transaction Costs

  • Jörn SassEmail author
  • Manfred Schäl
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 248)


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.


Numeraire portfolio Utility function Consistent price system Proportional transaction costs Dynamic programming 


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Fachbereich MathematikTU KaiserslauternKaiserslauternGermany
  2. 2.Institut für Angewandte MathematikUniversität BonnBonnGermany

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