Asymptotics and duality for the Davis and Norman problem

By Stefan Gerhold, Johannes Muhle‐Karbe, Walter Schachermayer. 2010

47 citations recorded by the source corpus.

We revisit the problem of maximizing expected logarithmic utility from consumption over an infinite horizon in the Black–Scholes model with proportional transaction costs, as studied in the seminal paper of Davis and Norman [Math. Operation Research, 15, 1990]. Similar to Kallsen and Muhle-Karbe [Ann. Appl. Probab., 20, 2010], we tackle this problem by determining a shadow price, that is a frictionless price process with values in the bid-ask spread which leads to the same optimization problem. However, we use a different parametrization that facilitates computation and verification. Moreover, for small transaction costs, we determine fractional Taylor expansions of arbitrary order for the boundaries of the no-trade region and the value function. This extends work of Janeček and Shreve [Finance Stoch., 8, 2004], who determined the leading terms of these power series.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/46d7d9ddad56258a0e0ec9f2e7aa0b9f9a65b42f

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Citations in the corpus

Duality theory for portfolio optimisation under transaction costs (2014, background): “Starting with the paper [32] of Kallsen and Muhle-Karbe, there have been explicit constructions of shadow prices for various concrete optimisation problems in the Black-Scholes model (see [22, 23, 21, 27, 7, 29]).”