Risk-sensitive control with HARA utility

Abstract

Abstract-In this paper, a control methodology based on the hyperbolic absolute risk averse (HARA) utility function is presented as an alternative to the exponential-of-an-integral approach to finding robust controllers. This work is inspired by the intuition that HARA controllers, while being robust, may give better performance than exponential controllers in normal situations. The HARA problem is shown to be equivalent to a certain differential game, and the asymptotic properties of the HARA problem and this differential game are studied. As an example, a linear-quadratic HARA problem is studied, where the problem of finding a robust HARA controller is proved to be equivalent to solving a standard linear-quadratic problem for a system with a higher noise intensity. This reveals an interesting relationship between robustness and uncertainty.

Stochastic maximum principle for partially observed risk‐sensitive optimal control problems of mean‐field forward‐backward stochastic differential equations

“…The theory in risk‐sensitive optimal control problems is so interesting and challenging and is also strongly related to robust, control theory, or portfolio optimization problems. There are many works on risk‐sensitive control problems, see Flemming, Soner, 34 Bielecki, Pliska, 35 Davis, Lleo, 36,37 Lim, Zhou, 38 and Whittle 39 . For the risk‐sensitive stochastic differential game of zero‐sum case, Reference 40 established a stochastic maximum principle for an open‐loop saddle point via nonlinear transformations of the adjoint processes of the equivalent risk‐neutral stochastic zero‐sum differential game.…”

Risk-sensitive Optimization for Robust Quantum Controls

“…To alleviate the conflict between the desired precision and the high robustness, we propose in this paper the risk-sensitive (RS) optimization approach which is illuminated by classical control theory [23][24][25][26][27][28]. The training is made sensitive to the poor-performance uncertainty samples, which takes both the advantages of the cases subject to the average error and the worst-case error.…”

Target-sensitive control of Markov and semi-Markov processes

“…Measures used to model risk in the Markov decision process (MDP) include variance [24,28,41], exponential utility functions [6,8,18,19,21,22,26,30,31], downside risk constraints [2,13,25,44,45], value at risk [7] and HARA utility functions [35]. Markowitz pioneered the popular use of variance in portfolio models: maximize E( ) Var( ) Revenues…”