Catastrophe Aversion and Risk Equity in an Interdependent World

Catastrophe aversion and risk equity are important concepts in both risk management theory and practice. Keeney (1980) was the first to formally define these concepts. He demonstrated that the two concepts are always in conflict. Yet this result is based on the assumption that individual risks are independent and has thus limited relevance for real world catastrophic events. We extend Keeney’s result to dependent risks and derive the conditions under which more correlation between two risks induces a more catastrophic risk. We then generalize some of the results for multiple correlated risks.

[1]  Antoine Bommier,et al.  Can preferences for catastrophe avoidance reconcile social discounting with intergenerational equity? , 2008, Soc. Choice Welf..

[2]  J. Darroch.  On the Distribution of the Number of Successes in Independent Trials , 1964 .

[3]  Ralph L. Keeney,et al.  Equity and Public Risk , 1980, Oper. Res..

[4]  Peter C. Fishburn,et al.  Equity Axioms for Public Risks , 1984, Oper. Res..

[5]  John A. Weymark,et al.  Shared destinies and the measurement of social risk equity , 2010, Ann. Oper. Res..

[6]  M. Rothschild,et al.  Some further results on the measurement of inequality , 1973 .

[7]  P. Fishburn,et al.  Dispersive equity and social risk , 1991 .

[8]  Ralph L. Keeney,et al.  Evaluating Decision Strategies for Equity of Public Risks , 1985, Oper. Res..

[9]  Bruno H. Strulovici,et al.  Increasing interdependence of multivariate distributions , 2012, J. Econ. Theory.

[10]  A. Tchen.  Inequalities for distributions with given marginals , 1976 .

[11]  Thorsten Rheinländer.  Risk Management: Value at Risk and Beyond , 2003 .

[12]  Rakesh Kumar Sarin,et al.  Technical Note - Measuring Equity in Public Risk , 1985, Oper. Res..

[13]  Ludger Rüschendorf,et al.  How robust is the value-at-risk of credit risk portfolios? , 2015 .

[14]  Larry G. Epstein,et al.  Increasing Generalized Correlation: A Definition and Some Economic Consequences , 1980 .

[15]  Nicolas Treich,et al.  Attitudes Toward Catastrophe , 2017 .

[16]  P. Embrechts,et al.  Risk Management: Correlation and Dependence in Risk Management: Properties and Pitfalls , 2002 .

[17]  L. Cox.  Why Income Inequality Indexes Do Not Apply to Health Risks , 2012, Risk Analysis.

[18]  Peter C. Fishburn,et al.  Equity Considerations in Public Risks Evaluation , 1989, Oper. Res..

[19]  EVALUATING LIFE OR DEATH PROSPECTS , 2012, Economics and Philosophy.

[20]  Ludger Rüschendorf,et al.  Computation of sharp bounds on the distribution of a function of dependent risks , 2012, J. Comput. Appl. Math..

[21]  Baruch Fischhoff,et al.  Modeling the Societal Impact of Fatal Accidents , 1984 .

[22]  M. Rothschild,et al.  Increasing risk: I. A definition , 1970 .

[23]  Nicolas Treich,et al.  The Social Value of Mortality Risk Reduction: Vsl vs. the Social Welfare Function Approach* , 2012 .

[24]  David G. Rand,et al.  Individual versus systemic risk and the Regulator's Dilemma , 2011, Proceedings of the National Academy of Sciences.

[25]  R. Wright.  Expectation dependence of random variables, with an application in portfolio theory , 1987 .

[26]  Samuel Karlin,et al.  Generalized convex inequalities , 1963 .

[27]  Isaac Meilijson,et al.  Convex majorization with an application to the length of critical paths , 1979, Journal of Applied Probability.

[28]  Marc Fleurbaey,et al.  Assessing Risky Social Situations , 2010, Journal of Political Economy.

[29]  P. Fishburn,et al.  Fairness and social risk I: unaggregated analyses , 1994 .