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1.3.5 Further Structure

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Parts II and III divide portfolio pricing from allocation considerations. Within each part, we further distinguish classical from modern approaches, and theory from practice. The hierarchy, reflected in the sequence of eight core chapters, is:

 Chapters 8 and 9: classical portfolio pricing theory and practice,

 Chapters 10 and 11: modern portfolio pricing theory and practice,

 Chapters 12 and 13: classical price allocation theory and practice, and

 Chapters 14 and 15: modern price allocation theory and practice.

Our dividing line between classical and modern is 1997, the average publication date of three highly influential papers. Relating to Part I: Artzner et al. (1997) introduced coherent risk measures and revolutionized thinking about measuring risk. Relating to Part II: Wang (1996) introduced the premium density and developed the theory of pricing by layer. And, relating to Part III: Phillips, Cummins, and Allen (1998) rigorously derived financial prices in a multiline company accounting for default. The classical versus modern bifurcation serves a convenient organizational purpose but should not be taken too seriously.

Classical pricing is predominantly actuarial and risk theoretic. A stability requirement, often linked to the probability of eventual ruin, determines required assets. There is no direct consideration of the cost of capital. On the other hand, modern approaches combine risk theory with financial and mathematical economics and decision science. They relate risk to the investors’ return and the cost of capital and pay attention to uncertainty and risk under pooling. They leverage powerful mathematics to understand intuitively reasonable risk measures.

Pricing Insurance Risk

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