Seminar Event Detail

Financial/Actuarial Mathematics

Date:  Wednesday, March 09, 2016
Location:  1360 East Hall (4:00 PM to 5:00 PM)

Title:  Optimal Control of Conditional Value-at-Risk in Continuous Time

Abstract:   We consider continuous-time stochastic optimal control problems featuring Conditional Value-at-Risk (CVaR) in the objective. The major difficulty in these problems arises from time-inconsistency, which prevents us from directly using dynamic programming. To resolve this challenge, we convert to an equivalent bilevel optimization problem in which the inner optimization problem is standard stochastic control. Furthermore, we provide conditions under which the outer objective function is convex and differentiable. We compute the outer objective's value via a Hamilton-Jacobi-Bellman equation and its gradient via the viscosity solution of a linear parabolic equation, which allows us to perform gradient descent. The significance of this result is that we provide an efficient dynamic programming-based algorithm for optimal control of CVaR without lifting the state-space. To broaden the applicability of the proposed algorithm, we provide convergent approximation schemes in cases where our key assumptions do not hold and characterize relevant suboptimality bounds. In addition, we extend our method to a more general class of risk metrics, which includes mean-variance and median-deviation. We also demonstrate a concrete application to portfolio optimization under CVaR constraints. Our results contribute an efficient framework for solving time-inconsistent CVaR-based dynamic optimization.

This is a joint work with Insoon Yang


Speaker:  Chris Miller
Institution:  UC Berkeley

Event Organizer:   Erhan Bayraktar


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