On using shadow prices in portfolio optimization with transaction costs

By Jan Kallsen, Johannes Muhle‐Karbe. 2010

113 citations recorded by the source corpus.

In frictionless markets, utility maximization problems are typically solved either by stochastic control or by martingale methods. Beginning with the seminal paper of Davis and Norman [Math. Oper. Res. 15 (1990) 676--713], stochastic control theory has also been used to solve various problems of this type in the presence of proportional transaction costs. Martingale methods, on the other hand, have so far only been used to derive general structural results. These apply the duality theory for frictionless markets typically to a fictitious shadow price process lying within the bid-ask bounds of the real price process. In this paper, we show that this dual approach can actually be used for both deriving a candidate solution and verification in Merton's problem with logarithmic utility and proportional transaction costs. In particular, we determine the shadow price process.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/beb9350a5e5443477b06e58fe0806b8b0f5973ff

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In Management Science and Operations Research

Citations in the corpus

Duality theory for portfolio optimisation under transaction costs (2014, background): “is a shadow price in the sense of the subsequent definition (compare [16, 17]).”
Asymptotics and duality for the Davis and Norman problem (2010, methodology): “This follows verbatim as in the proof of [[14], Theorem 4.”