A multi-state reserving model of motor insurance claims of an insurance company in Ghana

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April, 2016
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General insurance under which motor insurance falls is perhaps the fastest grow-ing area thus claim numbers and amount are huge (Achieng, 2010). Due to the high rate of growth, number of claims are also overwhelming thus creating a huge backlog of unsettled claims. The objective of the study was to explore how the multistate model underlie the development of motor insurance contracts using a three state model, the states being Incurred But Not Reported (IBNR), Reported But Not Settled (RBNS) and PAID. The three state model was used to derive the expressions for transition probabilities using the generator matrix and the Chapman-Kolmogorov forward di erential equations. This was done after the transition rates had been estimated using the method of maximum likelihood. These were then used to compute the number of claims in the development years. It was found that losses arrived at the IBNR state at a rate of 105 losses per month and then waits for 1.88 months before it transitions to the RBNS state with a force of 0.53 claims per month. Claims reported were then seen to be set- tled (PAID) with the force of settlement of 0.17 claims per month. All the claims in the IBNR states were moved to the RBNS in the accident year, 80 percent of claim in the RBNS state are settled in the accident year with the remaining spread over three more years. 44.6 percent and 47.2 percent of the claims are paid in the accident and rst development year respectively. It was concluded that an average of 6 claims are reported per year with 2 claims being settled in the same year. The claims in the IBNR state are run o after a year, claims in the RBNS and PAID states being completely run o after four and ve years respectively. Expressions for the expected number of claims for the accident year and development years were derived.
A thesis submitted to The Department of Mathematics, Kwame Nkrumah University of Science and Technology in partial fulfillment of the requirement for the degree of Master of Science, Actuarial Science.