Paper: arXiv 2604.00472

Authors: Wenyuan Li, Haoqi Lyu

Abstract

This paper investigates the valuation of variable annuity contracts with an early surrender option under non-Markovian models. Moreover, policyholders are provided with guaranteed minimum maturity and death benefits to protect against the downside risk. Unlike the existing literature, our variable annuity account value is linked to two non-Markovian processes: an equity index modeled by a rough Heston model and a force of mortality following a Volterra-type stochastic model. In this case, the early surrender feature introduces an optimal stopping problem where continuation values depend on the entire path history, rendering traditional numerical methods infeasible. We develop a deep signature Least Squares Monte Carlo approach to learn optimal surrender strategies on a discretized time grid. To mitigate the curse of dimensionality arising from the path-dependent model, we use truncated rough-path signatures to encode the historical paths and approximate the continuation values using a neural network. Numerically, we find that the fair fee increases with the Hurst parameters of both the stock volatility and the force of mortality. Finally, a convergence proof is provided to further support the stability of our method.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 4.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a mathematically sophisticated framework combining rough Heston models, Volterra mortality processes, and deep signature neural networks for optimal stopping. While it includes theoretical convergence proofs and detailed numerical experiments, it relies primarily on simulated dynamics rather than extensive empirical backtesting with historical market data.

Research Flowchart

  flowchart TD
    A[Research Goal: Value Variable Annuities with Early Surrender under Non-Markovian Models] --> B[Inputs: Rough Heston Stock Index & Volterra Mortality Model]
    B --> C[Methodology: Formulate Optimal Stopping Problem with Path-Dependent Continuation Values]
    C --> D[Feature Engineering: Truncate Rough-Path Signatures to Compress Path History]
    D --> E[Computation: Train Neural Network via Deep Signature Least Squares Monte Carlo]
    E --> F[Findings: Proved Method Convergence & Found Fair Fees Increase with Hurst Parameters]

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and 44 more
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  8. Valuation of guaranteed minimum maturity benefits under generalised regime-switching models using the Fourier Cosine method (2022)
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5 of 52 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.