On the uniqueness of solutions of stochastic Volterra equations
Probability
2020-05-01 v2 Mathematical Finance
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.
Keywords
Cite
@article{arxiv.1912.05917,
title = {On the uniqueness of solutions of stochastic Volterra equations},
author = {Alexandre Pannier and Antoine Jacquier},
journal= {arXiv preprint arXiv:1912.05917},
year = {2020}
}
Comments
The proof of Proposition 3.6, on Page 10 -- part 3 of the proof -- contains an erroneous inequality