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University of Manchester Contingencies 1 Lecture week 11 30 April 2014 “Revision”

University of Manchester Contingencies 1 Lecture week 11 30 April 2014 “Revision”. MATH20962 Jon Ferns FIA Jon.ferns@btinternet.com 077 89 487 194 Version 29 April 2014. Agenda. Slides: Reserves Death Strain at risk Loss random variables UDD, CFM Non annual premiums

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University of Manchester Contingencies 1 Lecture week 11 30 April 2014 “Revision”

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  1. University of ManchesterContingencies 1Lecture week 1130 April 2014“Revision” MATH20962 Jon Ferns FIA Jon.ferns@btinternet.com 077 89 487 194 Version 29 April 2014

  2. Agenda Slides: • Reserves • Death Strain at risk • Loss random variables • UDD, CFM • Non annual premiums • Functions of mu and delta

  3. When is tV calculated? Time t-1 Time t Time t+1 Benefit payment (and related expenses) Premium payment (and related expenses) tV

  4. Reserves

  5. Reserves

  6. Recursive relationship between reserves

  7. Re-arranging the recursive formula:Death Strain at Risk (Sum at Risk)

  8. Mortality Profit

  9. Loss as a random variable (recap)

  10. Non-integer ages - UDD

  11. Non-integer ages - UDD

  12. Non-integer ages - CFM

  13. Monthly annuities

  14. tpx as an integral of mx

  15. Compound interest / Functions of d, m, tpx fTx(t)

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