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The ultimate drawdown insurance and its state-dependent premium

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  • Xu, Duo
  • Li, Shu

Abstract

The analysis of drawdown risk is attracting growing interest thanks to its valuable insights into risk management. In this paper, we analyze an insurance contract designed to provide protection against the risk of market drawdown, where the claim is triggered by an ultimate drawdown. The concept of the ultimate drawdown was introduced in Li and Zhou (2022), which occurs either when the drawdown size exceeds a soft barrier for an extended period (so-called the Parisian drawdown), or when the drawdown size exceeds a significantly hard barrier. We propose the state-dependent premium structure for the ultimate drawdown insurance, where the premium are collected when the underlying process is in the financial non-distress state. Under the Lévy insurance framework, we analytically derive the fair market premium for the proposed premium structure. Furthermore, we explore the policyholder’s optimal surrender strategy when the contract allows for a cancellation feature. We demonstrate the merits of the proposed premium structure on the surrender risk, by comparing it to the constant premium structure. Numerical examples are provided for illustration. In addition, we examine some drawdown-related penalty functions of interest.

Suggested Citation

  • Xu, Duo & Li, Shu, 2026. "The ultimate drawdown insurance and its state-dependent premium," Insurance: Mathematics and Economics, Elsevier, vol. 126(C).
    • Handle: RePEc:eee:insuma:v:126:y:2026:i:c:s0167668725001477
    DOI: 10.1016/j.insmatheco.2025.103201
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