An HJB Approach to a General Continuous-Time Mean-Variance Stochastic Control Problem
Probability
2019-05-16 v3 Optimization and Control
Abstract
A general continuous mean-variance problem is considered for a diffusion controlled process where the reward functional has an integral and a terminal-time component. The problem is transformed into a superposition of a static and a dynamic optimization problem. The value function of the latter can be considered as the solution to a degenerate HJB equation either in viscosity or in Sobolev sense (after a regularization) under suitable assumptions and with implications with regards to the optimality of strategies. There is a useful interplay between the two approaches -- viscosity and Sobolev.
Cite
@article{arxiv.1508.05835,
title = {An HJB Approach to a General Continuous-Time Mean-Variance Stochastic Control Problem},
author = {Georgios Aivaliotis and Alexander Yu. Veretennikov},
journal= {arXiv preprint arXiv:1508.05835},
year = {2019}
}