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On non-negative solutions of stochastic Volterra equations with jumps and non-Lipschitz coefficients

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  • Aur'elien Alfonsi
  • Guillaume Szulda

Abstract

We consider one-dimensional stochastic Volterra equations with jumps for which we establish conditions upon the convolution kernel and coefficients for the strong existence and pathwise uniqueness of a non-negative c\`adl\`ag solution. By using the approach recently developed in arXiv:2302.07758, we show the strong existence by using a nonnegative approximation of the equation whose convergence is proved via a variant of the Yamada--Watanabe approximation technique. We apply our results to L\'evy-driven stochastic Volterra equations. In particular, we are able to define a Volterra extension of the so-called alpha-stable Cox--Ingersoll--Ross process, which is especially used for applications in Mathematical Finance.

Suggested Citation

  • Aur'elien Alfonsi & Guillaume Szulda, 2024. "On non-negative solutions of stochastic Volterra equations with jumps and non-Lipschitz coefficients," Papers 2402.19203, arXiv.org, revised Jul 2024.
    • Handle: RePEc:arx:papers:2402.19203
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    References listed on IDEAS

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