Implementing portfolio risk management and hedging in practice

ArXiv ID: 2309.15767 “View on arXiv”

Authors: Unknown

Abstract

In academic literature portfolio risk management and hedging are often versed in the language of stochastic control and Hamilton–Jacobi–Bellman~(HJB) equations in continuous time. In practice the continuous-time framework of stochastic control may be undesirable for various business reasons. In this work we present a straightforward approach for thinking of cross-asset portfolio risk management and hedging, providing some implementation details, while rarely venturing outside the convex optimisation setting of (approximate) quadratic programming~(QP). We pay particular attention to the correspondence between the economic concepts and their mathematical representations; the abstractions enabling us to handle multiple asset classes and risk models at once; the dimensional analysis of the resulting equations; and the assumptions inherent in our derivations. We demonstrate how to solve the resulting QPs with CVXOPT.

Keywords: Stochastic Control, Hamilton-Jacobi-Bellman (HJB) Equations, Quadratic Programming (QP), CVXOPT, Portfolio Risk Management, Cross-Asset

Complexity vs Empirical Score

  • Math Complexity: 4.0/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Street Traders
  • Why: The paper presents a practical quadratic programming framework with implementation details (CVXOPT) and focus on business constraints, indicating strong empirical rigor, but avoids advanced stochastic calculus in favor of accessible linear algebra, keeping math complexity moderate.
  flowchart TD
    A["Research Goal: Develop a practical approach for cross-asset portfolio risk management using optimization"] --> B["Methodology: Approximate Quadratic Programming QP instead of Stochastic Control/HJB"]
    B --> C["Input: Portfolio Data & Risk Models"]
    C --> D["Process: Dimensional Analysis & Economic-Mathematical Correspondence"]
    D --> E["Computation: Solve QP using CVXOPT"]
    E --> F["Outcome: Practical hedging framework for multiple asset classes"]