The Efficient Dual-Limit Liability Insurance Contract

Conventional liability insurance typically applies a single per occurrence limit to a given set of verbally described lawsuits against the insured. This Demonstration explores the circumstances under which the insured would prefer to divide the set of lawsuits that might be brought against it into two categories (A and B) and have potentially different liability limits applied to each. The top panel shows the possible outcomes of the two categories of lawsuits that might be brought against the insured. The left panel shows the cost of accidents (premiums plus monetized value of residual risk) for all combinations of per occurrence limits against categories A and B and identifies the optimal contract. The right panel shows the cost of accidents for all possible conventional liability insurance contracts in which the same per occurrence limit is used regardless of whether the lawsuit falls into category A or B. The cost of accidents should never be higher for the dual-limit policy than for the single-limit policy and often proves lower. Although the differences look small, given that liability insurance premiums amount to hundreds of billions of dollars worldwide, even modest percentage savings from finer classifications would be absolutely significant, if such classifications could be accomplished.