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Why demand for high ded policies incr?
- trend toward self-ins to provide savings to insd
- insd tx saving since liability for ins ded on unpd clm is tax ded
- positive cash flow to insr
- reduction of assessments for residual mkt pools
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Deductible vs excess policies
- ded usually for smaller retentions for risk w high frequency. Insr settles loss and is reimb for ded
- excess usually for high retention, self ins. Insr only settles clms over retention
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Calculation of ELR (ded / xs policy)
- straight ded: k = [Lr + (N-n)r] / L
- k = LER, N = # clm, n = # clm < retention, Lr = loss < ret
- disappearing ded: k = {Lr + LR - (LR - rNR) / [R / (R - r)]} / L
- LR =
loss btwn r and R, NR = # clms btwn r and R - fk = tempered LER (insr still responsible if insd can't pay)
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Determination of discount (D = 1 - P' / P) (ded policy)
- assume A, T, P proportional to P
- assume other exp are fixed portions of full cov prem
- P = [(E - a)P + eP] / (1 - A - T - p)
- P' = [(1 - fk)(E - a)P + eP] / (1 - A - T - p)
- D = fk(E - a) / (1 - A - T - p)
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Determination of discouts (xs policy)
- case 1: A, T, p, i, u, gh prop to P, other are fixed
- P = (EP + eP) / (1 - A - T - p - i - u - gh)
- P' = [(1 - fk)EP + eP] / (1 - A - T - p - i - u - gh)
- D = fkE / (1 - A - T - p - i - u - gh)
- case 2: A, T, p prop to P, i, u, gh prop to XS loss, other fixed
- D = fkE(1 + iE + uE + ghE) / (1 - A - T - P)
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Determination of discount (ex-med covg)
- LER only applies to med PP
- ex-med PP = total PP - portion of med PP
- why portion: adverse selctn, may req pmt of some med, liable
- only A and T are prop to P, other expenses not reduced
- P = (E + eP) / (1 - A - T)P' = (E - kEM + eP) / (1 - A - T)
- D = [(1 - A - T - e) / (1 - A - T)] * (kEM / E)
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Adjustment under retro rating
- c' = adjusted loss conversion factor so that loss dollars provided by c = loss dollars from c of ex-med pol
- let J = c - 1, J' = c' - 1 = J * E / (E - kEM)
- J' = J(1 - A - T - e) / [(1 - D)(1 - A - T) - e]
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