Develops a Hilbert space-valued Markovian lift framework for stochastic Volterra equations and establishes existence of limit distributions, LLN with convergence rate, and CLT for time averages in the Gaussian domain.
Lifting of Volterra processes: Optimal control in UMD Banach spaces.arXiv:2306.14175v1, 2023
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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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Limit theorems for stochastic Volterra processes
Develops a Hilbert space-valued Markovian lift framework for stochastic Volterra equations and establishes existence of limit distributions, LLN with convergence rate, and CLT for time averages in the Gaussian domain.
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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.