D-TIPO: Deep time-inconsistent portfolio optimization with stocks and options

ArXiv ID: 2308.10556 “View on arXiv”

Authors: Unknown

Abstract

In this paper, we propose a machine learning algorithm for time-inconsistent portfolio optimization. The proposed algorithm builds upon neural network based trading schemes, in which the asset allocation at each time point is determined by a a neural network. The loss function is given by an empirical version of the objective function of the portfolio optimization problem. Moreover, various trading constraints are naturally fulfilled by choosing appropriate activation functions in the output layers of the neural networks. Besides this, our main contribution is to add options to the portfolio of risky assets and a risk-free bond and using additional neural networks to determine the amount allocated into the options as well as their strike prices. We consider objective functions more in line with the rational preference of an investor than the classical mean-variance, apply realistic trading constraints and model the assets with a correlated jump-diffusion SDE. With an incomplete market and a more involved objective function, we show that it is beneficial to add options to the portfolio. Moreover, it is shown that adding options leads to a more constant stock allocation with less demand for drastic re-allocations.

Keywords: Portfolio Optimization, Neural Networks, Derivatives, Time-Inconsistency, Jump-Diffusion

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 5.0/10
  • Quadrant: Holy Grail
  • Why: The paper involves advanced mathematics like jump-diffusion SDEs, time-inconsistent stochastic control, and neural network approximations, yet it focuses on backtest-ready methodology with realistic constraints and numerical experiments, though it lacks live trading metrics.
  flowchart TD
    A["Research Goal: Incorporate Options in Time-Inconsistent Portfolio Optimization"] --> B["Methodology: Deep Learning w/ Neural Networks"]
    B --> C["Inputs: Correlated Jump-Diffusion SDE Data"]
    C --> D["Computation: NN Allocation & Options Pricing"]
    D --> E["Constraints: Rational Preferences & Trading Limits"]
    E --> F["Outcomes: Improved Returns & Constant Stock Allocation"]