Annuity Equivalent Wealth and the decision to subscribe private individual annuities

We model the demand for private annuities following Yaari (1965). In the line of Brown (1999) we define an Annuity Equivalent Wealth (AEW) that reflects the fact that an annuity provides a greater utility to a risk adverse individual than an actuarially equivalent lump sum. This indicator depends on the mortality risk, the level of risk aversion and the level of SS benefits. We develop Brown's approach to account for the valuation of bequests and for adverse selection on the market for annuities. We simulate this indicator on a sample of singles aged between 45 and 59 from the Patrimoine Survey (1998). Under the assumption that insurers will not propose actuarially fair premia (which may be explained by legal constraints in France), we find a strong correlation between the Annuity Equivalent Wealth and the decision to subscribe private individual annuities.