Prediction of reserves using multivariate power-normal mixture distribution - Ang, Siew Ling *; Pooi, Ah Hin * (AIP Publishing, 2016)

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Recently, in the area on stochastic loss reserving, there are a number of papers which analyze the individual claims data using the Position Dependent Marked Poisson Process. The present paper instead uses a different type of individual data. For the i-th (1 ≤ i ≤ n) customer, these individual data include the sum insured i s together with the amount paid ij y and the amount ij a reported but not yet paid in the j-th (1 6) j dd development year. A technique based on multivariate power-normal mixture distribution is already available for predicting the future value ( 1 ijy , 1 ija ) using the present year value(,) i j i j ya and the sum insured i s . Presently the above technique is improved by the transformation of distribution which is defined on the whole real line to one which is non-negative and having approximately the same first four moments as the original distribution. It is found that, for the dataset considered in this paper, the improved method giveV a better estimate for the reserve when compared with the chain ladder reserve estimate. Furthermore, the method is expected to provide a fairly reliable value for the Provision of Risk Margin for Adverse Deviation (PRAD)