Paper: arXiv 2402.14100

Abstract

In this note we consider the maximization of the expected terminal wealth for the setup of quadratic transaction costs. First, we provide a very simple probabilistic solution to the problem. Although the problem was largely studied, as far as we know up to date this simple and probabilistic form of the solution has not appeared in the literature. Next, we apply the general result for the numerical study of the case where the risky asset is given by a fractional Brownian Motion and the information flow of the investor can be diversified.

Complexity vs Empirical Score

  • Math Complexity: 9.5/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a highly theoretical solution using advanced stochastic calculus and martingale theory without any real-world data or backtesting, focusing on a mathematical derivation for an idealized liquidation model.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Maximize expected terminal wealth<br>with quadratic transaction costs"] --> B{"Methodology"}
  
  B --> C["Probabilistic Solution Derivation<br>Mathematical derivation for general case"]
  B --> D["Numerical Application<br>Apply to Fractional Brownian Motion<br>with diversified information flow"]
  
  C --> E["Key Findings<br>1. Simple probabilistic form<br>2. Novel result in literature"]
  D --> F["Key Findings<br>1. Application framework established<br>2. Numerical implementation ready"]
  
  E --> G["Outcomes<br>Contribution to Portfolio Optimization<br>and Optimal Execution Theory"]
  F --> G
  
  style A fill:#e1f5fe
  style G fill:#f3e5f5

Cited References (21)

  1. High-frequency trading with fractional Brownian motion (2020) — link
  2. Gaussian processes with Volterra kernels (2020) — link
  3. Trading Fractional Brownian Motion (2019) — link
  4. Optimal trade execution in order books with stochastic liquidity (2018) — link
  5. Optimal Investment with Transient Price Impact (2018) — link
  6. Hedging with temporary price impact (2015) — link
  7. Hedging, Arbitrage, and Optimality with Superlinear Frictions (2015) — link
  8. Optimal Trade Execution under Geometric Brownian Motion in the Almgren and Chriss Framework (2011) — link
and 13 more
  1. Fractals and Scaling In Finance: Discontinuity, Concentration, Risk (2010) — link
  2. Arbitrage in fractional Brownian motion models (2003) — link
  3. An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions (1999) — link
  4. Arbitrage with Fractional Brownian Motion (1997) — link
  5. Noise (1931)
  6. Gaussian Volterra processes with power-type kernels. Part I (2022) — link
  7. Arbitrage with fractional Brownian motion (2007)
  8. Optimal execution for portfolio transactions (2006)
  9. Optimal execution of portfolio trans-actions (2000) — link
  10. Stock market prices and long-range dependence (1999) — link
  11. Fractals and Scaling in Finance (1997) — link
  12. Stock Price Returns and the Joseph Effect: A Fractional Version of the Black-Scholes Model (1995) — link
  13. Semimartingale Theory and Stochastic Calculus (1992) — link

0 of 21 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.