| The study of the optimal relative premium of the Bonus-malus system usually under theinfinite time (stationary state). However,to some extent, It can reflect optimal property of theBonus-malus system,the policyholders insured time is limited.So it is realistic to study theoptimal relative premium of the bonus-malus system in finite time.Additionally, considering the prior characteristic and the random effects of the applicantare not always the same,they vary with time,accordingly,the Claim frequency is no longer aconstant. So the homogeneous Markova chain can not be used to depict the track of the levelof the Bonus-malus system. Then we have to resort to the non-homogeneous Markov chain.As the result, the classical algorithm for the optimal relative premium based on steady-statedistribution is no longer applicable. So it is necessary to find a formula for the optimalrelative premium under conditions of dynamic heterogeneity.Based on the research of N. Brouhns, m. Guille en, m. Denuit&J. Pinquet (2002) andBarczy&Pap (2011), the optimal relative premium in finite time under the dynamic randomeffects reliability model is studied.Above all,the distribution function of random effect isfound under the assumption that the random effect is a second-order auto-regressive randomsequence.In addition, assuming that only limited years is considered (T years), then everyyear have a transition probability matrix. The annual transition probability matrix has asteady-state distribution, this steady-state probability distribution can be used to calculate anoptimal relative premium. Then, the weighted average premium of those T years can becalculated, it is a better optimal relative premium in finite time. But this formula of relativepremium is not very accurate,so a more accurate formula is found in the nextsubsection.Finally, the robustness of the optimal relative premium formula is discussed in thelast chapter. |
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