i need to create a transition matrix for a senario, i think ive figured out the state space, which in dependent on the last 2 states, bu I don't know how to put it into a matrix
1'31 1].]. I. UJ. lgllllll'llh 1 Background You are an actuarial analyst at AK Insurance. Your company offers a Bonus-Males System [EMS] [or also called his Claim Discount [NCDJJ car insurance scheme, which has 5,D policyholders in the current policy year [2021]. The base premium charged to policyholders is Milli per annum, before any discounts or penalties are applied. Your company has been modelling the transitions for all policyholders in the current portfolio using a discrete-lime Markos chain. From a previous analysis, you can assume that the annual number of claims for each policyholder is independent and follows a Poisson distribution with expected claims frequency parameter Jt = {14. Moreover, you can assume that the sire of each claim is independent and follows a Gamma distribution with parameters or = 2 and f3 = .[l1 (that is, with mean '2,Dli]. The size of each claim is also independent of the annual number of claims. [Current EMS scheme] The details of the current HMS scheme are summarised below. There are ve levels of discount, summarised in the following table. New policyholders enter the sch-e on Discount Level ii. if policyholders have no claims during a year, they move up to the next higher discount level in the following year [subject to the highest Discount Level 2]. If policyholders have only one claim during a year, they move down to the next lower level of discount; and if they have two or more claims, then they move down two levels {subject to the inset Discount Level -2 in both cases]. 1four actuarial pricing team just had a meeting to discuss potential changes to the current scheme. Your manager is particularly interested in the following two ideas raised in the meeting. [Uption A] This modication aims to take into account a longer claim history of policyholders in providing discounts to them. A policyholder will move up to the next higher discount level in the following year only if they have two consecutive claim-free years, and remain in the current discount level if they have no claim only in the current year. For example, they will only move up a discount level in Elli? [subject to the highest Discount Level 2} if they have no claims in Edit] and il. if they have no claim in MEI but one or more claims in Will, they will remain in the same discount level in $122. The other transition rules remain unchanged, that is, if a policyholder has one claim during a year, they move down one discount level in the following year; and if they have two or more claims during a year, they move down two discount levels in the following year [subject to the lowest Discount Level -2 in both came]
