Weighted Scoring Rules and Convex Risk Measures
References
- (2012) Entropic value-at-risk: A new coherent risk measure. J. Optim. Theory Appl. 155(3):1105–1123.Crossref, Google Scholar
- (1999) Coherent measures of risk. Math. Finance 9(3):203–228.Crossref, Google Scholar
- (2015) Data-driven stochastic programming using phi-divergences. The Operations Research Revolution. Tutorials Oper. Res. 1–19.Google Scholar
- (2001) Strong one-switch utility. Management Sci. 47(4):601–604.Link, Google Scholar
- (1986) Expected utility, penalty functions, and duality in stochastic nonlinear programming. Management Sci. 32(11):1445–1466.Link, Google Scholar
- (2007) An old-new concept of convex risk measures: The optimized certainty equivalent. Math. Finance 17(3):449–476.Crossref, Google Scholar
- (2007) Some comparisons among quadratic, spherical, and logarithmic scoring rules. Decision Anal. 4(2):49–65.Link, Google Scholar
- (2010) Scoring rules and decision analysis education. Decision Anal. 7(4):346–357.Link, Google Scholar
- (2004) Convex Optimization (Cambridge University Press, New York).Crossref, Google Scholar
- (1970) Mathematical Methods in Risk Theory (Springer, Berlin).Google Scholar
- (2016) An overview of applications of proper scoring rules. Decision Anal. 13(4):223–242.Link, Google Scholar
- (2012) Solving the problem of inadequate scoring rules for assessing probabilistic football fore-cast models. J. Quant. Anal. Sports 8(1). https://doi.org/10.1515/1559-0410.1418.Google Scholar
- (1967) Information type measures of differences of probability distribution and indirect observations. Studia Math. Hungarica 2:299–318.Google Scholar
- (2012) Proper local scoring rules on discrete sample spaces. Ann. Statist. 40(1):593–608.Crossref, Google Scholar
- (2002) Convex measures of risk and trading constraints. Finance Stochastics 6(4):429–447.Crossref, Google Scholar
- (2012) Compatible weighted proper scoring rules. Biometrika 99(4):989–994.Crossref, Google Scholar
- (2002) Putting order in risk measures. J. Bank. Finance 26(7):1473–1486.Crossref, Google Scholar
- (2018) Optimal expected utility risk measures. Stat. Risk Model 35(1-2):73–87.Crossref, Google Scholar
- (2007) Strictly proper scoring rules, prediction, and estimation. J. Amer. Statist. Assoc. 102(477):359–378.Crossref, Google Scholar
- (2001) Minimax and minimal distance martingale measures and their relationship to portfolio optimization. Finance Stochastics 5(4):557–581.Crossref, Google Scholar
- (2019) A probability scoring rule for simultaneous events. Decis. Anal. 16(4):301–313.Link, Google Scholar
- (2004) Game theory, maximum entropy, minimum discrepancy and robust bayesian decision theory. Ann. Statist. 32(4):1367–1433.Crossref, Google Scholar
- (2003) Combinatorial information market design. Inform. Systems Frontiers 5(1):107–119.Crossref, Google Scholar
- (1971) Proper scores for probability forecasters. Ann. Math. Statist. 42(6):1916–1921.Crossref, Google Scholar
- (2017) Focusing on regions of interest in forecast evaluation. Ann. Appl. Statist. 11(4):2404–2431.Crossref, Google Scholar
- (2006) Another look at measures of forecast accuracy. International Journal of Forecasting 22(4):679–688, ISSN 0169-2070, URL http://dx.doi.org/https://doi.org/10.1016/j.ijforecast.2006.03.001.Crossref, Google Scholar
- (2012) Log-optimal economic evaluation of probability forecasts. J. Roy. Stat. Soc. Series A (Statist. Soc.) 175(3):661–689.Crossref, Google Scholar
- (2011) Fitting probability forecasting models by scoring rules and maximum likelihood. J. Statist. Plann. Inference 141(5):1832–1837.Crossref, Google Scholar
- (2011) Tailored scoring rules for probabilities. Decision Anal. 8(4):256–268.Link, Google Scholar
- (2009) Evaluating quantile assessments. Oper. Res. 57(5):1287–1297.Link, Google Scholar
- (2008) Scoring rules, generalized entropy, and utility maximization. Oper. Res. 56(5):1146–1157.Link, Google Scholar
- (2004) Approximating risk aversion in decision analysis applications. Decision Anal. 1(1):51–67.Link, Google Scholar
- (1956) Measures of the value of information. Proc. Natl. Acad. Sci. USA 42(9):654–655.Crossref, Google Scholar
- (2007) Scoring rules, entropy, and imprecise probabilities. 5th International Sympos. Imprecise Probability, vol. 7, 307–315.Google Scholar
- (1900) On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. London Edinburgh Dublin Philos. Magazine J. Sci. 50(302):157–175.Crossref, Google Scholar
- (1970) Convex Analysis. Princeton Mathematical Series (Princeton University Press, Princeton, NJ).Crossref, Google Scholar
- (2007) Coherent approaches to risk in optimization under uncertainty. Tutorials Oper. Res. 3:38–61.Google Scholar
- (2000) Optimization of conditional value-at-risk. J. Risk 2:21–42.Crossref, Google Scholar
- (1971) Elicitation of personal probabilities and expectations. J. Amer. Statist. Assoc. 66(336):783–801.Crossref, Google Scholar
- (1998) Axiomatic characterization of the quadratic scoring rule. Experiment. Econom. 1(1):43–61.Crossref, Google Scholar
- (1968) “Good” probability assessors. J. Appl. Meteorol. 7(5):751–758.Crossref, Google Scholar
- (1996) Scoring rules and the evaluation of probabilities. TEST 5(1):1–60.Crossref, Google Scholar

