Chapter 18 ERA 2.2 Risk Measures and Capital Allocation - G. Venter

\(\star\) Risk measures and their pros/cons

• Moment based

• Tail based (\(VaR\), \(TVaR\), \(XTVaR\), \(EPD\)), see table 18.1

• Probability transform

  • e.g. Esscher (18.1)

• Generalized moments

Capital a company should hold depends on practical considerations, not simply derived from a risk measure

• e.g. Customer reactions, or keepin renewal business

Allocation of risk measures

• Definitions 18.2

• Proportional

• Co-measures, table 18.3 and 18.2

Allocation method properties:

• Marginal allocation 18.3

  • Scalable risk measures 18.4

• Suitable allocation 18.3

Marginal impact (18.4)

• A risk measure can have many co-measures but only 1 will be marginal

Allocation works best when the risk measure \(\propto\) the market value of risk

Can bypass the above if we can just allocate the cost of capital

• Option pricing or the MV of stop loss that attach at 0 profit