18.3 Required Capital

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

• Risk measures should be used to measure the safety of the capital

Considerations that drive capital requirements:

• Customers reactions:
  Well capitalized insurer \(\Leftarrow\) vs \(\Rightarrow\) better price
  Know your customer base, whether they are price or capital sensitive

  • \(\downarrow\) rating \(\Rightarrow\) \(\downdownarrows\) of cumtomers since customers that want a higher level can quickly leave

  • \(\uparrow\) rating \(\Rightarrow\) \(\upharpoonleft\) of growth since higher rating just provides an opportunity to compete with other insurers that already have the business

• Keeping renewal business:
  Have enough capital so that in adverse scenario there is still enough capital to service renewals that is x% of the business

  • Since renewal business are more profitable

Once capital level has been established, compare it against different risk measures

• Look at % of capital lost a various probability levels

• \(TVaR\) is a better risk measure than \(VaR\) for a given percentile since \(VaR\) is just the smallest loss XS of a percentile, \(TVaR\) is the average