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arXiv · 1912.05917

On the uniqueness of solutions of stochastic Volterra equations

Alexandre Pannier·Antoine Jacquier
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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.

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Alexandre Pannier, Antoine Jacquier. 2019-12-12. On the uniqueness of solutions of stochastic Volterra equations. https://arxiv.org/abs/1912.05917

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