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On the uniqueness of solutions of stochastic Volterra equations

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  • Alexandre Pannier
  • Antoine Jacquier

Abstract

We prove strong existence and uniqueness, and H\"older regularity, of a large class of stochastic Volterra equations, with singular kernels and non-Lipschitz diffusion coefficient. Extending Yamada-Watanabe's theorem, our proof relies on an approximation of the process by a sequence of semimartingales with regularised kernels. We apply these results to the rough Heston model, with square-root diffusion coefficient, recently proposed in Mathematical Finance to model the volatility of asset prices.

Suggested Citation

  • Alexandre Pannier & Antoine Jacquier, 2019. "On the uniqueness of solutions of stochastic Volterra equations," Papers 1912.05917, arXiv.org, revised Apr 2020.
    • Handle: RePEc:arx:papers:1912.05917
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    References listed on IDEAS

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