Sponsored Ads
Pauline Reimer, ASA, MAAA
Pryor Associates
Actuarial Openings: Life, P&C, Health, Pensions, Finance
Ezra Penland Actuarial Recruiters
Top Actuary Jobs
Salary Surveys Apply Bios Casualty Health Life Pension

Results 1 to 2 of 2

Thread: Problem with recursion

  1. #1
    Actuary.com - Level I Poster
    Join Date
    Oct 2006
    Posts
    18

    Problem with recursion

    Problem is taken from exams for Polish Actuaries from 10th October 2005, Exercice 1, General Insurance Mathematics. Here is the problem:

    Damage which occurred in year t is liquidated:
    - in the same year with probability 0.3
    - in the next year with probabilitu 0.3
    - in the year t+k (k>1) with probability 0.8 * (0.5)^k
    We don't care in which period of the year the damage occurred - e.g. if one damage occurred on the 1st January and any other damage occurred on 30th December the probability that they are liquidated by the end of the k-th year is the same.
    Let R(t) denotes the number of damages which were NOT liquidated at the end of the year t (R(t) consists both of the unliquidated damages which occurred in year t as well as of the unliquidated damages which occurred before the year t and weren't liquidated at the end of year t-1).
    Let n(t) denotes the number of damages in year t.
    Assuming that
    R(t-1) = 1100
    n(t) = 900
    n(t-1) = 800
    find the expected value of R(t) under the three conditions given above.

    Answer is R(t) =1220.

    The most sensible way of solving the problem seems to be finding the recursion formula for R(t) as the function of (R(t-1), n(t) and n(t-1).
    As I was trying to solve the problem I met with the problem that n(t-2) which value is not given couldn't be reduced. I suppose I do it in the wrong way and don't know what to do with it.
    If anyone could help me with this exercice I'll be extremely grateful.

    Nobody1111
    Last edited by Nobody1111; May 10th 2007 at 01:16 PM.

  2. #2
    Actuary.com - Level II Poster
    Join Date
    Mar 2007
    Posts
    59
    I don't see how it can be solved recursively. I can reduce it to R(t) = 1760 - .5 R(t-2) - .05 n(t-2), but I don't think there is enough information for a recursive approach. I thought I was on to something when I managed to make the infinite sums go away...The only thing I can think of is that you could use a distribution type to determine E[X], but that is probably a dead end, too. If you find the answer, please share.

Thread Information

Users Browsing this Thread

There are currently 1 users browsing this thread. (0 members and 1 guests)

Similar Threads

  1. Practic Exam "FM" Problems - courtesy Actex Publications and Richard L. London, FSA
    By admin in forum SOA Exam FM / CAS Exam 2 - Financial Mathematics - with practice exam problems
    Replies: 8
    Last Post: September 20th 2007, 12:04 PM
  2. Problem of the week question
    By jstarderfan in forum SOA Exam P / CAS Exam 1 - Probability - with practice exam problems
    Replies: 10
    Last Post: March 29th 2007, 01:35 AM
  3. Mortality problem
    By Nobody1111 in forum SOA Exam MLC - Actuarial Models, Life Contingencies - with practice exam problems
    Replies: 3
    Last Post: December 17th 2006, 08:50 PM
  4. question on Exam P problem
    By SCIGEEK in forum Actuarial Exams - General Discussion
    Replies: 5
    Last Post: February 15th 2006, 09:54 AM
  5. Sample Exam "CAS/4" Problems - courtesy of Sam Broverman and Actex
    By admin in forum SOA Exam C / CAS Exam 4 - Construction + Evaluation of Models - with practice exam problems
    Replies: 0
    Last Post: April 12th 2005, 10:18 AM

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •