Claims Reserving Manual, vol.2: Section D7: Probability distribution of outstanding liability from individual payments data

Document description

Many stochastic claims reserving methods use aggregate data and yield the first two moments (best estimate and standard error) of the outstanding liability. The term "aggregate data" here refers to the total of payments made for each cohort and each stage of development as opposed to the amount of each individual payment. This paper describes an approach which differs from most stochastic reserving methods in both these respects:

• (i) it makes use of data on the amount of each individual payment (rather than aggregate data)
• (ii) it yields a complete probability distribution for the total outstanding liability (rather than just the first two moments).

The advantage of point (ii) is that more complete information is provided for setting the claims reserve. For most purposes, a claims reserve should include an allowance for possible adverse experience rather than being purely the "best estimate" (that is, the first moment, or expected value). This extra allowance is analogous to a safety load (or risk load) in (re) insurance pricing, and we shall use this terminology.