Paper: arXiv 2305.11319

Abstract

We define and develop an approach for risk budgeting allocation - a risk diversification portfolio strategy - where risk is measured using a dynamic time-consistent risk measure. For this, we introduce a notion of dynamic risk contributions that generalise the classical Euler contributions and which allow us to obtain dynamic risk contributions in a recursive manner. We prove that, for the class of coherent dynamic distortion risk measures, the risk allocation problem may be recast as a sequence of strictly convex optimisation problems. Moreover, we show that self-financing dynamic risk budgeting strategies with initial wealth of 1 are scaled versions of the solution of the sequence of convex optimisation problems. Furthermore, we develop an actor-critic approach, leveraging the elicitability of dynamic risk measures, to solve for risk budgeting strategies using deep learning.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper develops a theoretical framework for dynamic risk budgeting using advanced concepts like coherent dynamic distortion risk measures, Gâteaux derivatives, and strictly convex optimization, leading to a high math complexity. However, the empirical implementation is limited to a conceptual deep learning actor-critic approach with illustrative examples, lacking detailed backtest results, code, or statistical metrics, resulting in low empirical rigor.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Risk Budgeting for Dynamic Risk Measures"] --> B["Methodology:<br>Define Dynamic Risk Contributions & Convex Optimization"]
  B --> C["Input:<br>Multi-Asset Portfolio Data"]
  C --> D["Process:<br>Actor-Critic Deep Learning Algorithm"]
  D --> E["Outcome:<br>Time-Consistent Dynamic Risk Budgeting Strategy"]