2019年4月英国精算师-风险模型真题

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  8 April 2019 (am)

  

  Subject CS2B – Risk Modelling and Survival Analysis Core Principles


  Data is available for the movement of taxis in London. The city is divided into three zones “North”, “South” and “West”. The movement of a taxi from one zone to another will depend only on its current position. The following probabilities have been determined for taxi movements:


  • Of all taxis in the North zone, 30% will remain in North and 30% will move to South, with the remaining 40% moving to West.


  • In the South zone, taxis have a 40% chance of moving to North, 40% chance of staying in South and 20% chance of moving to West.


  • Of all the drivers in the West zone, 50% will move to North and 30% to South with the remaining 20% staying in West.


  The movement of taxis in London will be modelled in R using a Markov Chain.


  (i) Create a vector with the state space of the Markov Chain, using R code. You should print this to the screen and paste into your answer.


  (ii) Construct a transition matrix of the zone movement probabilities. You should print this to the screen and paste into your answer.


  (iii) Load the R package for Markov Chains and paste your coding into your answer.


  (iv) Create a Markov Chain object with state space equal to your vector in part (i) and transition matrix from part (ii). You should print this to the screen and paste into your answer.


  The transition diagram for the Markov Chain is shown below:



  (v) Calculate the probability that a driver currently in the North zone will be in the North zone after:


  (a) two trips


  (b) three trips.


  (vi) Determine the stationary state of the Markov Chain.



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