A note on large deviations in life insurance

TL;DR

This paper investigates large deviations in life insurance portfolios with non-identically distributed, bounded losses, providing exponential bounds on tail probabilities but showing that a full large deviation principle does not hold under these conditions.

Contribution

It introduces bounds for large deviations in life insurance portfolios without assuming identical distribution, highlighting limitations of existing principles.

Findings

Established exponential bounds for average loss exceeding thresholds.

Showed that a full large deviation principle does not follow from the assumptions.

Provided a counterexample illustrating the limitations of the bounds.

Abstract

We study large and moderate deviations for a life insurance portfolio, without assuming identically distributed losses. The crucial assumption is that losses are bounded, and that variances are bounded below. From a standard large deviations upper bound, we get an exponential bound for the probability of the average loss exceeding a threshold. A counterexample shows that a full large deviation principle does not follow from our assumptions.