Dependence uncertainty affects risk evaluation in joint life insurance

What the study found

The study found that, for some standard joint life insurance contracts, risk evaluation based on a distortion risk measure is monotone with respect to the concordance order of the underlying copula, which is a way to describe dependence between two lifetimes. The authors also report that bounds for the mean, Value-at-Risk, and Expected Shortfall can be computed by combinations of linear programs when dependence uncertainty is described by a norm-ball centered on a reference copula.
What the authors say this matters
The authors say this matters because dependence among lifetimes is important for pricing and evaluating joint life insurance products, and limited data can make the dependence structure uncertain. The study suggests that the proposed bounds can improve existing bounds based on the available information.
What the researchers tested
The researchers studied robust pricing and risk evaluation of joint life insurance products under uncertainty about the dependence between two lifetimes. They analyzed standard contracts, distortion risk measures, concordance order of copulas, and an uncertainty set defined as a norm-ball around a reference copula.
What worked and what didn't
The monotonicity result held for some class of standard contracts. Using that result, the authors derived the most conservative and anti-conservative risk evaluations for that class, and showed that bounds for the mean, Value-at-Risk, and Expected Shortfall can be computed through combinations of linear programs under the specified uncertainty set.
Their numerical analysis found that sensitivity to the choice of copula differs depending on the risk measure and the type of contract. They also found that their proposed bounds can improve existing bounds based on the available information.
What to keep in mind
The abstract does not describe all contract types covered, so the monotonicity result is stated only for some standard contracts. Other limitations are not described in the available summary.