Paper: arXiv 2407.07100

Abstract

We propose a general approximation method for determining optimal trading strategies in markets with proportional transaction costs, with a polynomial approximation of the residual value function. The method is exemplified by several problems from optimally tracking benchmarks, hedging the Log contract, to maximizing utility from terminal wealth. Strategies are also approximated by practically executable, discrete trades. We identify the necessary trade-off between trading frequency and trade sizes to have satisfactory agreement with the theoretically optimal, continuous strategies of infinite activity.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper is heavily math-centric, featuring advanced asymptotic methods, free boundary problems, and reflected diffusions without any empirical backtests, datasets, or implementation details.

Research Flowchart

  flowchart TD
  A["Research Goal: Approximate optimal trading strategies with transaction costs"] --> B{"Methodology: Polynomial Approximation"}
  B --> C["Input: Market models & cost structure"]
  B --> D["Input: Objective function e.g. utility or tracking error"]
  C & D --> E["Process: Solve DP/HJB for residual value"]
  E --> F["Process: Approximate solution via polynomial expansion"]
  F --> G["Outcome: Discrete executable trading strategy"]
  G --> H["Key Finding: Optimal trade-off between frequency and size"]

Cited References (22)

  1. Almost Perfect Shadow Prices — → 2401.00970
  2. Leveraged funds: robust replication and performance evaluation (2023) — link
  3. The Alpha Engine: Designing an Automated Trading Algorithm (2017) — link
  4. The limits of leverage (2015) — link
  5. Nonlinear price impact and portfolio choice (2015) — link
  6. Asymptotics for fixed transaction costs (2013) — link
  7. THE GENERAL STRUCTURE OF OPTIMAL INVESTMENT AND CONSUMPTION WITH SMALL TRANSACTION COSTS (2013) — link
  8. Portfolio Choice with Transaction Costs: A User’s Guide (2012) — link
and 14 more
  1. Transaction costs, trading volume, and the liquidity premium (2011) — link
  2. Asymptotics and duality for the Davis and Norman problem (2010) — link
  3. The dual optimizer for the growth-optimal portfolio under transaction costs (2010) — link
  4. On characterisation of Markov processes via martingale problems (2006) — link
  5. Handbook of Brownian Motion - Facts and Formulae (1996) — link
  6. Optimal Investment and Consumption with Transaction Costs (1994) — link
  7. The Log Contract (1994) — link
  8. A Diffusion Model for Optimal Portfolio Selection in the Presence of Brokerage Fees (1988) — link
  9. Stopped Random Walks: Limit Theorems and Applications (1987)
  10. Capital Market Equilibrium with Transaction Costs (1986) — link
  11. Smooth investment (2016) — link
  12. ‘Why is the effect of proportional transaction costs δ 2 / 3 ? (2004)
  13. Stochastic differential equations with reflecting boundary condition in convex regions (1979) — link
  14. ii) Maximal trades: These strategies reset a portfolio statistic to its target value once it reaches these boundaries (cf. the first second plot in Figure 1

1 of 22 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.