On the uniqueness of solutions of stochastic Volterra equations

2019/12/12 by Alexandre Pannier, Pannier, Alexandre, Antoine Jacquier +1
Economics, Econometrics and Finance · Mathematics · #60G22 #60H10 #91G80 #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Mathematical Finance (q-fin.MF) #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1912.05917

openalex publication_date 2019/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove strong existence and uniqueness, and Hölder 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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