Loss Reserving Using Loss Aversion Functions

The tradeoff insurance premium as a two-sided generalisation of the distortion premium

“…Equal weighting φ = 1 leads to the original expected loss E(x). Choo and De Jong (2009) show the equivalence between loss aversion reserves, distortion premiums and spectral risks.…”

“…ToP generalises loss aversion reserves (Choo and De Jong, 2009), distortion premiums (Wang, 1996) and spectral risks (Acerbi, 2002) by assigning higher penalty weights to loss outcomes further from a ''loss appetite'' rather than to larger loss outcomes. Penalty weights forming the ToP are aligned with cumulative prospect theory (Tversky and Kahneman, 1992), where extreme outcomes, relative to a reference point, are magnified and moderate outcomes are diminished.…”

“…Proofs are given in Wang (1996) and Choo and De Jong (2009). In contrast the dual is superadditive: the premium increases upon aggregation since undesired smaller severities are diversified:…”

“…The mapping is used to calculate insurance premiums or manage risk. An example premium principle is the loss aversion reserve (Choo and De Jong, 2009), a weighted average loss where weights are a non-decreasing function of the loss percentile rank. Loss aversion reserves are equivalent to distortion premiums (Wang, 1996) and spectral risks (Acerbi, 2002).…”

“…Examples in this paper express the ToP as a two-sided generalisation of one-sided premiums or risks, including Valueat-Risk, conditional-tail-expectation and expected-maximal-loss (Choo and De Jong, 2009). The two-sided generalisation reflects the undesirability of both small and large loss outcomes, with the loss appetite controlling their relative representation in the ToP.…”