# An overview of optimal control optimization problems driven by non-convexity measures

@article{Wang2020AnOO, title={An overview of optimal control optimization problems driven by non-convexity measures}, author={Weixin Wang}, journal={arXiv: Optimization and Control}, year={2020} }

Recently, literature on dynamic coherent risk measures has broadened the choices for risk-sensitive performance evaluation. A running example includes Cumulative prospect theory and Conditional variance at risk. Most of them can be can be interpreted in general as a non-linear transformation of a given random variable. Non-convexity property has implied a lot of mathematical intricacies and challenges. The paper gives overview on the recent development of dynamic programming optimal control…

## References

SHOWING 1-10 OF 14 REFERENCES

### Risk Sensitive Markov Decision Processes

- Mathematics
- 1997

Risk-sensitive control is an area of significant current interest in stochastic control theory. It is a generalization of the classical, risk-neutral approach, whereby we seek to minimize an…

### PORTFOLIO CHOICE VIA QUANTILES

- Economics
- 2010

A portfolio choice model in continuous time is formulated for both complete and incomplete markets, where the quantile function of the terminal cash flow, instead of the cash flow itself, is taken as…

### Cumulative Prospect Theory Meets Reinforcement Learning: Prediction and Control

- Computer ScienceICML
- 2016

This work bringsulative prospect theory to a risk-sensitive reinforcement learning (RL) setting and designs algorithms for both estimation and control and provides theoretical convergence guarantees for all the proposed algorithms.

### Stochastic Optimization in a Cumulative Prospect Theory Framework

- Computer ScienceIEEE Transactions on Automatic Control
- 2018

This paper proposes both gradient based as well as gradient-free CPT-value optimization algorithms that are based on two well-known simulation optimization ideas: simultaneous perturbation stochastic approximation and model-based parameter search, respectively.

### Prospect theory: an analysis of decision under risk — Source link

- Economics
- 2007

This paper presents a critique of expected utility theory as a descriptive model of decision making under risk, and develops an alternative model, called prospect theory. Choices among risky…

### Advances in prospect theory: Cumulative representation of uncertainty

- Economics
- 1992

We develop a new version of prospect theory that employs cumulative rather than separable decision weights and extends the theory in several respects. This version, called cumulative prospect theory,…

### Prospect Theory: For Risk and Ambiguity

- Economics
- 2010

Preface Introduction Part I. Expected Utility: 1. The general model of decision under uncertainty no-arbitrage (expected utility with known utilities and unknown probabilities) 2. Expected utility…

### On the Theory of Dynamic Programming.

- MathematicsProceedings of the National Academy of Sciences of the United States of America
- 1952

This paper is the text of an invited address before the annual summer meeting of the American Mathematical Society at Laramie, Wyoming, September 2, 1954, of an expository nature on the theory of dynamic programming.