7  Expenses

posts/070-expenses.qmd

Compiled: 2026-02-28 09:50:53.962676500

It is unrealistic for a monograph on pricing to entirely exclude expenses. Thus far, we have considered a net or technical premium, which includes a risk and profit load but excludes other acquisition and administrative expenses. In this section, we consider the impact of expenses and generate a gross premium.

7.1 Kinds of Expenses

posts/070-files/expenses.qmd

7.1.1 Acquisition

7.1.2 General and Administrative

7.1.3 Claims

7.1.4 Investment

7.2 Expense Bases

7.3 Premium Formulas Including Expenses

The premium \(P\) is net of expenses. It can be combined with a fixed expense \(F\) and variable expense rate \(e\) to determine a gross premium \[ G = \frac{P + F}{1 - e}. \] \(G\) is best understood by writing down the sources and uses of premium \[ G = P + F + eG = L + R + S + F + eG \] where the (risk) profit margin \(P - L = R + S\) is decomposed into a risk margin \(R\) and service margin \(S\). In this section we are concerned only with \(P\).

Table 7.1: Source and use of gross premiums.

Source of Funds	Use of Funds
\(L\)	Pay losses to policyholder and claims expenses
\(R\)	Compensation to capital for bearing risk
\(S\)	Compensation to paper for organizing insurance service; fronting
\(F\)	Fixed, per policy, expense allocations
\(eG\)	Commission (customer), premium tax (paper) and other proportional expenses

There are no additional assumptions needed for the GAAP statements.