@article{markowitz1952portfolio,
	Author = {Markowitz, H.},
	Journal = {The Journal of Finance},
	Number = {1},
	Pages = {77--91},
	Publisher = {Wiley Online Library},
	Title = {Portfolio selection},
	Volume = {7},
	Year = {1952}}
@inproceedings{tamar2015coherent,
	author = {Tamar, A. and Chow, Y. and Ghavamzadeh, M. and Mannor, S.},
	booktitle = {Advances in Neural Information Processing Systems},
	pages = {1468--1476},
	title = {Policy Gradient for Coherent Risk Measures},
	volume = {28},
	year = {2015}
}
@article{prashanth2016mlj,
	Author = {Prashanth, L. A. and Ghavamzadeh, M.},
	Journal = {Machine Learning},
	Month = {Dec},
	Number = {3},
	Pages = {367--417},
	Title = {Variance-constrained Actor-critic Algorithms for Discounted and Average Reward {MDP}s},
	Volume = {105},
	Year = {2016}}

@inproceedings{tamar2012policy,
	Author = {Tamar, A. and Castro, D. D. and Mannor, S.},
	Booktitle = {{Proceedings of the Twenty-Ninth International Conference on Machine Learning}},
	Pages = {387-396},
	Title = {{Policy gradients with variance related risk criteria}},
	Year = {2012}}

 @inproceedings{borkar2010risk,
	Author = {Borkar, V. S. and Jain, R.},
	Booktitle = {{IEEE Conference on Decision and Control}},
	Pages = {2664--2669},
	Title = {{Risk-constrained Markov decision processes}},
	Year = {2010}}

 @inproceedings{borkar2010learning,
	Author = {Borkar, V. S.},
	Booktitle = {Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems--MTNS},
	Title = {Learning algorithms for risk-sensitive control},
	Volume = {5},
	Year = {2010}}

 @inproceedings{huang2017risk,
  title={{Risk-aware Q-learning for Markov decision processes}},
  author={Huang, W. and Haskell, W. B.},
  booktitle={2017 IEEE 56th Annual Conference on Decision and Control (CDC)},
  pages={4928--4933},
  year={2017},
  organization={IEEE}
}

@book{mood74,
  title={Introduction to the Theory of Statistics},
  edition={3rd},
  author={A. M. Mood and  and F. A. Graybill and D. C. Boes},
  publisher={McGraw Hill},
  year={1974},
}
@article{shalabh_book,
    author = {Bhatnagar, S. and Prasad, H. and Prashanth, L. A.},
    year = {2013},
    title = {Stochastic recursive algorithms for optimization. Simultaneous perturbation methods},
    volume = {434},
    journal = {Lecture Notes in Control and Inform. Sci.},
}
@inproceedings{wang02,
    title={A Risk Measure That Goes Beyond Coherence},
    author={Wang, SS},
    year={2002}
}
@inproceedings{sutton08,
    author = {Sutton, R. S. and Maei, H. and Szepesv\'{a}ri, C.},
    booktitle = {Adv. Neural Inf. Process. Syst.},
    title = {A Convergent O(n) Temporal-difference Algorithm for Off-policy Learning with Linear Function Approximation},
    volume = {21},
    year = {2009}
}
@article{zhangK2020,
    author    = {K. Zhang and A. Koppel and H. Zhu and T. Basar},
    title     = {Global Convergence of Policy Gradient Methods to (Almost) Locally Optimal Policies},
    journal   = {{SIAM} J. Control. Optim.},
    volume    = {58},
    number    = {6},
    pages     = {3586--3612},
    year      = {2020},
}
@article{denneberg1990,
    title={Distorted probabilities and insurance premiums},
    author={Denneberg, D.},
    journal={Methods of Operations Research},
    volume={63},
    number={3},
    pages={3--5},
    year={1990}
}

@article{tversky1992advances,
	Author = {Tversky, A. and Kahneman, D.},
	Journal = {J. Risk Uncertain.},
	Title = {Advances in prospect theory: Cumulative representation of uncertainty},
	Volume = {5},
	Year = {1992}
}
@article{rockafellar2000optimization,
	Author = {Rockafellar, R. T. and Uryasev, S.},
	Journal = {Journal of risk},
	Pages = {21--42},
	Title = {{Optimization of conditional value-at-risk}},
	Volume = {2},
	Year = {2000}
}
@article{balbas2009properties,
	title={Properties of distortion risk measures},
	author={Balb{\'a}s, A. and Garrido, J. and Mayoral, S.},
	journal={Methodology and Computing in Applied Probability},
	volume={11},
	number={3},
	pages={385--399},
	year={2009},
}

@article{dowd2006,
    author = {K. Dowd and D. Blake},
    title = {After VaR: The Theory, Estimation, and Insurance Applications of Quantile-Based Risk Measures},
    journal = {The Journal of Risk and Insurance},
    number = {2},
    pages = {193--229},
    volume = {73},
    year = {2006}
}
@article{ghadimi2013,
    title={Stochastic First- and Zeroth-Order Methods for Nonconvex Stochastic Programming},
    author={S. Ghadimi and G. Lan},
    journal={SIAM J. Optim.},
    year={2013},
    volume={23},
}
@article{chow2017risk,
	title={Risk-constrained reinforcement learning with percentile risk criteria},
	author={Chow, Y. and Ghavamzadeh, M. and Janson, L. and Pavone, M.},
    journal = {J. Mach. Learn. Res.},
	volume={18},
	number={1},
	pages={6070--6120},
	year={2017},
}
@inproceedings{prashanth2014cvar,
	Author = {Prashanth, L. A.},
	Booktitle = {Algorithmic Learning Theory (ALT)},
	Pages = {155--169},
	Title = {{Policy gradients for CVaR-constrained MDPs}},
	Year = {2014}
}
@article{Borkar02QR,
	Author = {V. S. Borkar},
	Journal = {Mathematics of Operations Research},
	Pages = {294--311},
	Title = {Q-learning for Risk-sensitive Control},
	Volume = {27},
	Year = {2002}
}
@article{acerbi2002spectral,
	title={Spectral measures of risk: A coherent representation of subjective risk aversion},
	author={Acerbi, C.},
	journal={Journal of Banking \& Finance},
	volume={26},
	number={7},
	pages={1505--1518},
	year={2002},
}
@article{jones03,
    author = {Jones, B. and Zitikis, R.},
    year = {2003},
    title = {Empirical Estimation of Risk Measures and Related Quantities},
    volume = {7},
    journal = {North American Actuarial Journal},
}
@article{wirch03,
    author = {Wirch, J. and Hardy, M.},
    year = {2003},
    pages = {168--168},
    title = {Distortion risk measures: Coherence and stochastic dominance},
    volume = {32},
    journal = {Insur. Math. Econ.}
}
@article{gzyl06,
    author = {Gzyl, H. and Mayoral, S.},
    year = {2008},
    title = {On a relationship between distorted and spectral risk measures},
    volume = {15},
    pages = {8--21},
   journal ={Revista de Economía Financiera}
}
@article{wang95,
title = {Insurance pricing and increased limits ratemaking by proportional hazards transforms},
author = {Wang, S.},
year = {1995},
journal = {Insur. Math. Econ.},
volume = {17},
number = {1},
pages = {43--54},
}
@article{wang96,
 title={Premium Calculation by Transforming the Layer Premium Density},
 volume={26},
 number={1},
 journal={ASTIN Bulletin},
 author={Wang, S.},
 year={1996},
 pages={71--92}
}
@aticle{wang97,
    title = {Axiomatic characterization of insurance prices},
    author = {Wang, S. S. and Young, V. R. and Panjer, H. H.},
    year = {1997},
    journal = {Insur. Math. Econ.},
    volume = {21},
    number = {2},
}
@article{gao18,
    author = {Gao, X. and Jiang, B. and Zhang, S.},
    title = {On the Information-Adaptive Variants of the ADMM: An Iteration Complexity Perspective},
    year = {2018},
    volume = {76},
    number = {1},
    journal = {J. Sci. Comput.},
    pages = {327--363},
}
@inproceedings{tamar2015,
    author = {Tamar, A. and Chow, Y. and Ghavamzadeh, M. and Mannor, S.},
    booktitle = {Adv. Neural Inf. Process. Syst.},
    title = {Policy Gradient for Coherent Risk Measures},
    year = {2015}
}
@book{nesterov_book,
    author    = {Y. E. Nesterov},
    title     = {Introductory Lectures on Convex Optimization - {A} Basic Course},
    series    = {Applied Optimization},
    volume    = {87},
    year      = {2004},
}
@inproceedings{prashla13,
    author = {Prashanth, L.A. and Ghavamzadeh, M.},
    booktitle = {Adv. Neural Inf. Process. Syst.},
    title = {Actor-Critic Algorithms for Risk-Sensitive MDPs},
    volume = {26},
    year = {2013}
}

@InProceedings{prashla16,
    title = 	 {Cumulative Prospect Theory Meets Reinforcement Learning: Prediction and Control},
    author = 	 {L.A. Prashanth and C. Jie and M. Fu and S. Marcus and C. Szepesvari},
    booktitle = {ICML},
    pages = 	 {1406--1415},
    year = 	 {2016},
    volume = 	 {48},
}
@article{spall1992,
    author={J. C. Spall},
    journal={IEEE Transactions on Automatic Control},
    title={Multivariate stochastic approximation using a simultaneous perturbation gradient approximation},
    year={1992},
    volume={37},
    number={3},
    pages={332--341}
}
@InProceedings{papini2018,
    title = {Stochastic Variance-Reduced Policy Gradient},
    author = {Papini, M. and Binaghi, D. and Canonaco, G. and Pirotta, M. and Restelli, M.},
    booktitle = {ICML},
    year = {2018},
}
@inproceedings{shen2019hessian,
    title={Hessian aided policy gradient},
    author={Shen, Z. and Ribeiro, A. and Hassani, H. and Qian, H. and Mi, C.},
    booktitle={ICML},
    pages={5729--5738},
    year={2019},
}
@article{katkovnik1972,
    author={Katkovnik, V.  and  Kulchitsky, Y.},
    year={1972},
    title={Convergence of a class of random search algorithms},
    journal={Autom. Remote. Control.},
    volume={33},
    issue= {8}
}
@article{nesterov2017,
    author={Nesterov, Y. and Spokoiny, V.},
    year={2017},
    title={Random Gradient-Free Minimization of Convex Functions},
    journal={Found. Comut. Math.},
    pages={527-- 566},
    volume={17},
    issue={2},
}
@inproceedings{flaxman,
    author = {Flaxman, A. D. and Kalai, A. T. and McMahan, H. B.},
    title = {Online Convex Optimization in the Bandit Setting: Gradient Descent without a Gradient},
    year = {2005},
    booktitle = {ACM-SIAM Symposium on Discrete Algorithms},
    pages = {385--394},
}
@article{shamir,
    author = {Shamir, O.},
    title = {An Optimal Algorithm for Bandit and Zero-Order Convex Optimization with Two-Point Feedback},
    year = {2017},
    volume = {18},
    number = {1},
    journal = {J. Mach. Learn. Res.},
    pages = {1703--1713},
}
@article{artzner99,
    author = {Artzner, P. and Delbaen, F. and Eber, J. and Heath, D.},
    title = {Coherent Measures of Risk},
    journal = {Mathematical Finance},
    volume = {9},
    number = {3},
    pages = {203--228},
    year = {1999}
}
@book{ndp_book,
    author = {Bertsekas, D. P. and Tsitsiklis, J. N.},
    title = {Neuro-Dynamic Programming},
    year = {1996},
    publisher = {Athena Scientific},
    edition = {1st}
}
@article{kim_2010,
    author = {Kim, J.},
    year = {2010},
    pages = {198--205},
    title = {Bias correction for estimated distortion risk measure using the bootstrap},
    volume = {47},
    journal = {Insur.: Math. Econ.},
}

@article{prashla2021,
    author={Prashanth, L.A. and Fu, M.},
    title={Risk-Sensitive Reinforcement Learning via Policy Gradient Search},
    year={2022},
    volume={15},
    number={5},
    journal={Foundations and Trends in Machine Learning},
    pages={537--693}}

@article{glynn21,
    author = {Glynn, P. and Peng, Y. and Fu, M. and Hu, J.},
    year = {2021},
    title = {Computing Sensitivities for Distortion Risk Measures},
    journal = {INFORMS J. Comp.}
}

@inproceedings{holland22,
    title = 	 { Spectral risk-based learning using unbounded losses },
    author =       {Holland, M. J. and Mehdi Haress, E.},
    booktitle = 	 {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics},
    pages = 	 {1871--1886},
    year = 	 {2022},
    volume = 	 {151},
    series = 	 {Proceedings of Machine Learning Research},
}
@article{nv2023,
    title={A policy gradient approach for optimization of smooth risk measures},
    author={N. Vijayan and L.A. Prashanth},
    year={2023},
    journal={arXiv preprint arXiv:2202.11046},
}
@article{nv2021,
    title={Policy gradient methods for distortion risk measures},
    author={N. Vijayan and L.A. Prashanth},
    year={2023},
    journal={arXiv preprint arXiv:2107.04422},
}
@article{nv1,
    title = {Smoothed functional-based gradient algorithms for off-policy reinforcement learning: A non-asymptotic viewpoint},
    author={N. Vijayan and L.A. Prashanth },
    journal = {Systems \& Control Letters},
    volume = {155},
    pages = {104988},
    year = {2021},
    issn = {0167-6911},
}