Siewert Loss Ratio method
Expected XS losses = Deductible Loss Charge + Aggregate Loss Charge
Deductible Loss Charge = Prem * ELR * excess ratio Chi
Aggregate Loss Charge = Prem * ELR * (1-Chi) * Aggregate Ratio Phi
Siewert Implied Development Method
Given unlimited and limited triangles, calculate LDFs and CDFs for each
Calculate ultimates for each, then get the layer ultimates by subtracting. Similar process for layer reserves.
Siewert Direct Development Method
Given unlimited and limited triangles as well as ratio of limited severity to unlimited severity, Rlim
LDFunlim = Rlim* LDFlim + (1-Rlim) * XSLDF
Solve for XSLDF
XS Losses = XSLDF * Losses in Layer
Siewert Credibility Weighting Method; BF cred weights
Given age-to-age factors and Rlims at different times
XSLDF = LDFt * (1-Rult)/(1-Rlimt)
Then project to Ult; this is the chainladder side
Expected Loss = Prem * ELR * Chi
Z = 1/XSLDF -> %paid; standard BF maneuver
Calc BF ult as usual
Unlimited/Limited/Excess LDF Relationships
RLt = Limited Severity t / Unlimited Severity t
Calc for both times you’re interested in getting the LDF between
Excess losses:
XSLDF t1 - t2 = LDFunlimited t1-t2 * (1-RLt2) / (1-RLt1)
Losses below deductible:
LDF lim t1-t2 = LDFunlimited t1-t2 * RL2/RL1
LDF unlimited t1-t2 = RL1 * LDF lim T1-t2 + (1-RL1) * XSLDF t1-t2
So it’s kind of like a cred weight with RL1
Siewert Distributional Model
Calculate unlimited LDF = Severityt2 / Severity t1
Option 1: Calc limited LDF with limited severities that same way
Option 2: Adjust unlimited LDF with severity relativities: LDFlim = LDFunlim * RL t2 / RLt1
XS LDF = Unlimited LDF * (1 - RelUlt) / (1 - Rel12)
Entry ratio
Aggregate Limit / Limited Loss
%Loss excess Deductible
1 - Limited Severity/E[Unlimited Severity]
Table M Adjustment
Adj = (1 + 0.8* %Loss excess Deduct) / (1 - %Loss excess Deduct)
Adjusted Limited Loss = E[Unlimited Loss] * Adj
Then see what Expected Loss Group these AdjLL fall into for Table M; Look up corresponding Insurance Charge Ratio with Entry Ratio
Insurance Charge = InsCharge Ratio * Limited Loss
Service Revenue Asset
Use distributional model to calc Limited CDFs and project Losses below Deductible up to ult value
Subtract off Aggregate Limit to get empirical excess losses
Use Collective Risk Model to get CDFs for excess losses and project the empirical data to excess ult; this LDF also becomes %reported weight
Use table to get Expected Excess loss value, then cred weight (with %rep on empirical data) the empirical with the expected to get Ult Excess Losses
Ult Deductible Losses Net of Aggregate = Ult Deductible - Ult Excess
Ult Recoverables = Ult DedLossNetAgg * Loss Multiplier
Service Revenue Asset = Ult Recoverables - Known Recoveries
Advantages of a High Deductible Program (5)
- Achieves pricing flexibility while passing additional risk to larger insureds
- Reduces residual market charges and premium taxes
- Gives cash flow advantages to insured
- Provides incentive for insureds to control losses while protecting them from large losses
- Allows “self-insurance” without subjecting insureds to demanding state requirements
Chi
Per-occurrence charge or excess ratio
