Viscosity Solutions Methods for Singular Perturbations in Deterministic and Stochastic Control
SIAM Journal on Control and Optimization
Bounds and Asymptotic Approximations for Utility Prices when Volatility is Random
SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Singular Perturbations in Ergodic Control of Diffusions
SIAM Journal on Control and Optimization
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We study singular perturbations of a class of stochastic control problems under assumptions motivated by models of financial markets with stochastic volatilities evolving on a fast time scale. We prove the convergence of the value function to the solution of a limit (effective) Cauchy problem for a parabolic equation of HJB type. We use methods of the theory of viscosity solutions and of the homogenization of fully nonlinear PDEs. We test the result on some financial examples, such as Merton portfolio optimization problem.