Linear-quadratic control for a class of stochastic Volterra equations: solvability and approximation

DOI10.1214/20-AAP1645zbMath1475.93116arXiv1911.01900MaRDI QIDQ2240882

Huyên Pham, Enzo Miller, Eduardo Abi Jaber

Publication date: 4 November 2021

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.01900

zbMATH Keywords

linear-quadratic controlstochastic Volterra equationsRiccati equations in Banach space

Mathematics Subject Classification ID

Fractional processes, including fractional Brownian motion (60G22) Optimal stochastic control (93E20) Linear-quadratic optimal control problems (49N10) Control/observation systems in abstract spaces (93C25) Stochastic integral equations (60H20)

Related Items (9)

Robust control in a rough environment ⋮ American Options in the Volterra Heston Model ⋮ Stochastic optimal control problems of discrete‐time Markov jump systems ⋮ Stochastic optimization of a mixed moving average process for controlling non-Markovian streamflow environments ⋮ Volterra square-root process: stationarity and regularity of the law ⋮ Linear-Quadratic Optimal Controls for Stochastic Volterra Integral Equations: Causal State Feedback and Path-Dependent Riccati Equations ⋮ On the maximum principle for optimal control problems of stochastic Volterra integral equations with delay ⋮ Modeling and computation of an integral operator Riccati equation for an infinite-dimensional stochastic differential equation governing streamflow discharge ⋮ Infinite horizon backward stochastic Volterra integral equations and discounted control problems

Cites Work

• Unnamed Item
• Unnamed Item
• Malliavin calculus and optimal control of stochastic Volterra equations
• Hedging with temporary price impact
• Direct solution of a Riccati equation arising in a stochastic control problem with control and observation on the boundary
• Fractional Brownian motion and the Markov property
• Perfect hedging in rough Heston models
• Generalized Feller processes and Markovian lifts of stochastic Volterra processes: the affine case
• Affine Volterra processes
• A martingale approach for fractional Brownian motions and related path dependent PDEs
• Markovian structure of the Volterra Heston model
• Affine representations of fractional processes with applications in mathematical finance
• Backward stochastic Volterra integral equations and some related problems
• Stochastic Volterra equations with anticipating coefficients
• Capacitary Measures for Completely Monotone Kernels via Singular Control
• Optimal Control for Stochastic Volterra Equations with Completely Monotone Kernels
• The stochastic Fubini theorem revisited
• About the linear-quadratic regulator problem under a fractional Brownian perturbation
• Volatility is rough
• Integral Operator Riccati Equations Arising in Stochastic Volterra Control Problems
• Lifting the Heston model
• Ambit Processes and Stochastic Partial Differential Equations
• Multifactor Approximation of Rough Volatility Models
• Linear quadratic control problems of stochastic Volterra integral equations
• Linear-Quadratic Fractional Gaussian Control

This page was built for publication: Linear-quadratic control for a class of stochastic Volterra equations: solvability and approximation