Paper: arXiv 2509.20239

Authors: Andrea Della Vecchia, Damir Filipović

Abstract

This paper investigates theoretical and methodological foundations for stochastic optimal control (SOC) in discrete time. We start formulating the control problem in a general dynamic programming framework, introducing the mathematical structure needed for a detailed convergence analysis. The associate value function is estimated through a sequence of approximations combining nonparametric regression methods and Monte Carlo subsampling. The regression step is performed within reproducing kernel Hilbert spaces (RKHSs), exploiting the classical KRR algorithm, while Monte Carlo sampling methods are introduced to estimate the continuation value. To assess the accuracy of our value function estimator, we propose a natural error decomposition and rigorously control the resulting error terms at each time step. We then analyze how this error propagates backward in time-from maturity to the initial stage-a relatively underexplored aspect of the SOC literature. Finally, we illustrate how our analysis naturally applies to a key financial application: the pricing of American options.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper is highly mathematically dense, featuring rigorous proofs, analysis in RKHS, and detailed error decomposition. Empirically, it focuses on algorithmic implementation and error control for American option pricing, but lacks the extensive code/backtest details typical of fully street-ready trading papers.

Research Flowchart

  flowchart TD
  A["Research Goal: Stochastic Optimal Control & Error Propagation Analysis"] --> B["Methodology: SOC Formulation & Value Function Approximation"]
  B --> C["Data: Stochastic Processes / Monte Carlo Sampling"]
  C --> D["Computation: RKHS & Kernel Ridge Regression"]
  D --> E["Analysis: Error Decomposition & Backward Propagation"]
  E --> F["Application: American Option Pricing"]
  F --> G["Key Findings: Theoretical Convergence & Accurate Derivative Pricing"]

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