Some New Classes of Consistent Risk Measures

Many types of insurance premium principles and/or risk measures can be characterized by means of a set of axioms, which in many cases are rather arbitrarily chosen and not always in accordance with economic reality. In the present paper we gener alize Yaari's risk measure by relaxing his axioms. In addition, we derive translation invariant minimal Orlicz risk measures, which we call Haezendonck risk measures, and obtain sufficient conditions on the risk measure of Bernoulli risks to fulfill additivity and superadditivity properties for Orlicz premium principles.

[1]  H. Gerber,et al.  Some Inequalities for Stop-Loss Premiums , 1977, ASTIN Bulletin.

[2]  Jan Dhaene,et al.  The Concept of Comonotonicity in Actuarial Science and Finance: Applications , 2002 .

[3]  Marc Goovaerts,et al.  Insurance premiums: Theory and applications , 1984 .

[4]  M. Yaari.  The Dual Theory of Choice under Risk , 1987 .

[5]  M. Goovaerts,et al.  A new premium calculation principle based on Orlicz norms , 1982 .

[6]  Jan Dhaene,et al.  A Unified Approach to Generate Risk Measures , 2003, ASTIN Bulletin.

[7]  Virginia R. Young,et al.  Ordering risks: Expected utility theory versus Yaari's dual theory of risk , 1998 .

[8]  Hans U. Gerber,et al.  An introduction to mathematical risk theory , 1982 .

[9]  Jan Dhaene,et al.  Modern Actuarial Risk Theory , 2001 .

[10]  Jan Dhaene,et al.  The Concept of Comonotonicity in Actuarial Science and Finance: Theory , 2002, Insurance: Mathematics and Economics.

[11]  William S. Jewell,et al.  Gerber Hans U.: An Introduction to Mathematical Risk Theory Huebner Foundation Monograph No. 8. Homewood, Ill.: Richard D. Irwin Inc., 1980, xv + 164, paperbound, $ 15.95 , 1980, ASTIN Bulletin.

[12]  Shaun S. Wang.  Premium Calculation by Transforming the Layer Premium Density , 1996, ASTIN Bulletin.

[13]  Jan Dhaene,et al.  Economic Capital Allocation Derived from Risk Measures , 2002 .

[14]  Marc Goovaerts,et al.  Insurance: Mathematics and Economics , 2006 .

[15]  On additive principles of zero utility , 1985 .