Almost Perfect Shadow Prices

Research output: Contribution to journalArticlepeer-review

Abstract

Shadow prices simplify the derivation of optimal trading strategies in markets with transaction costs by transferring optimization into a more tractable, frictionless market. This paper establishes that a naïve shadow price ansatz for maximizing long-term returns, given average volatility yields a strategy that is, for small bid–ask spreads, asymptotically optimal at the third order. Considering the second-order impact of transaction costs, such a strategy is essentially optimal. However, for risk aversion different from one, we devise alternative strategies that outperform the shadow market at the fourth order. Finally, it is shown that the risk-neutral objective rules out the existence of shadow prices.

Original languageEnglish
Article number70
JournalJournal of Risk and Financial Management
Volume17
Issue number2
DOIs
Publication statusPublished - Feb 2024

Keywords

  • portfolio choice
  • reflected diffusions
  • shadow prices
  • transaction costs

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