Bivariate nearly-unstable Hawkes processes with distinct roughness exponents converge weakly to a coupled stochastic Volterra equation driven by two Brownian motions, with an explicit cross-kernel.
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The value function for optimal control of non-convolution Volterra integral diffusions is characterized as the unique viscosity solution to a parabolic PDE on Sobolev space, with applications to time-inconsistent contract problems.
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Scaling Limits of Bivariate Nearly-Unstable Hawkes Processes and Applications to Rough Volatility
Bivariate nearly-unstable Hawkes processes with distinct roughness exponents converge weakly to a coupled stochastic Volterra equation driven by two Brownian motions, with an explicit cross-kernel.
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Optimal control of Volterra integral diffusions and application to contract theory
The value function for optimal control of non-convolution Volterra integral diffusions is characterized as the unique viscosity solution to a parabolic PDE on Sobolev space, with applications to time-inconsistent contract problems.