Formulae Flashcards
Earned premiums
Written premiums
- Change in UPR (end-begin)
Claims incurred
Paid claims
+ change in reserves (end-begin)
Expenses incurred
Paid expenses
+ change in reserves (end-begin)
Underwriting profit
= earned premiums
- claims incurred
- expenses incurred
Benefit payment after the principle of average
(sum insured) / (value of risk)
x
(loss amount)
Proportion reinsured
(Net WP) / (Gross WP)
Or
(Net claims incurred) / (Gross claims incurred)
Expense ratio
(Expenses paid) / (Net written premium)
Loss ratio (claim ratio)
(Incurred claims) / (Earned premiums)
Or
(Claims paid from WP) / (Written premiums)
Commission rate
(Commission paid) / (Net written premiums)
Combined ratio (operating ratio or underwriting ratio)
Loss ratio + expense ratio
Investment return ratio
(Investment return amount) / (Average assets held)
Profit margin
(Insurance profit) / (NEP)
Return on Capital
(Profit after tax) / (Reserves at the start of the period)
Solvency ratio
(A - L) / (NWP)
Assets to liabilities
A:L
Claims settlement pattern
(Total outstanding claims reserve) / (Claims paid)
The technical account (the revenue account)
Premiums earned
(Claims incurred)
(Expenses incurred)
Change in DAC
= Underwriting profit
+ Investment income
= Insurance profit
Net premiums earned
Gross premiums written
(Reinsurance premiums paid)
(Change in UPR)
= Premiums earned
Net claims incurred
Gross claims paid
(Reinsurance and other recoveries)
Change in RBNS
= claims incurred
Net expenses incurred
Expenses paid
Change in expense provision
(Reinsurance commissions received)
= net expenses incurred
The Profit and Loss account
Insurance profit
Other investment income
Profits from other activities
(Interest on loans)
= Profit before tax
(Tax)
= Profit attributable to shareholders
(Dividends)
= Retained profits
The Balance Sheet
Fixed assets
Investments
Other current assets
= Total Assets
(Current liabilities)
(Deferred tax)
(Unearned premium reserve)
Deferred acquisition costs
(RBNS)
= (Total Liabilities)
= Shareholders’ Net Assets
Share capital
Share premium account
Profit and loss account
Revaluation reserve
= Shareholders’ funds
Amount of return commission
= (return commission %)(proportion ceded).(premium)
Ceding commission
= return commission + override commission
Proportion retained under surplus reinsurance
a = (retention amount) / (total amount) for every risk ceded
Largest risk the company can take on under surplus reinsurance
(maximum retention).(maximum number of lines)
= R.(1+L)
When we want to cede the maximum amount of a risk under a surplus treaty
(EML)/(k+1) = size of each line.
Cede k and retain 1
Rate on line (for XoL)
(total reinsurance premium charged, ignoring reinstatement premiums) / (width of layer)
UPR
(Premium - Acquisition costs).(Proportion of risk period unexpired)
AURR
Max(0, URR - UPR)
Premium liability
The larger of (aggregate of UPR for all lines of business) and (best estimate of URR)
Prediction variance
Process variance + Estimation variance
Premium rate
1) premium income/expected loss
2) premium income/limit
3) premium income/exposure
4) premium income/risk-adjusted exposure
Premium rate change
(Premium rate @T2 / Premium rate @ T1) - 1
Lapse rate
(# lapses) / (# renewals invited)
Renewal rate
(# renewals) / (# renewals invited)
New business rate
(# new policies) / (# renewals invited)
Strike rate
(# policies written) / (# quotes given)
Not-take-up rate
(# policies not struck) / (# quotes given)
Cancellation rate
1) (# policies cancelled) / (# policies exposed)
Gives a central rate
2) (# cancellations) / (# renewals invited)
Gives an initial rate
Endorsement rate
(# endorsements) / (# policies exposed)
Credibility-weighted estimate
Estimate of future claims =
Z.(observations) + (1-Z).(other information)
Z = credibility
1-Z = complement of credibility
Burning cost premium
(total claims) / ( total exposed to risk)
Effective burning cost premium
Burning cost using unadjusted data
Indexed burning cost
Burning cost using adjusted data
Pure risk premium
(expected claim frequency).(expected cost per claim)
[(#claims)/(#policies) ÷
(exposure)/(#policies)] x (total claim amount)/(#claims)
Relative loss severity
Y = X/M
Relative loss severity = size of loss / size of risk
Liability outgo
Total gross claim payments
(Reinsurance and other recoveries)
Expenses
(Outstanding premiums received)
Tax and dividend payments
