Recoveries

• #Salvage & Subrogation
• #Reinsurance

Salvage & Subrogation

• Data availability impacts S&S Estimation
  • Treated as negative payments else recorded separately
  • Capture different types separately or combine all types together
  • Some estimate Case O/S for recoveries. Some don't.¹

\(\text{Recoverable S\&S} = \text{Ult. S\&S} -\text{Received S\&S}\), same as unpaid S&S.

Approaches

• Development (or any in Section G) on S&S \(\triangle\)
  • Works better for salvage (as it develops quickly) \(\to\) Property coverage
  • than subrogation (takes longer to develop) \(\to\) Liability coverage
• Ratio Approach
  • Develop \(\dfrac{\text{S\&S}}{\text{Gross Claims}}\)
  • Apply ratio to ultimate claim estimates \(\to\) Project S&S

Accident	Developed	Selected	Ult	Received	Recoverable
Year	S&S ratio	S&S ratio	S&S	S&S	S&S
2006	0.361	36.10%	$6,137.00	$5,600.19	$536.81
2007	0.381653	38.17%	$6,583.51	$5,900.27	$683.24
2008	0.3718	37.18%	$6,134.70	$2,700.13	$3,434.57
Recoverable S&S					$4,654.62
- We have to provide a selection rationale for each… e.g. 2006 and 2007 are nearly developed so it is inappropriate to select any other
- Default judgement: Select ratios based on the ratio CDFs for each year
- If downward trend: "Assume insurer is recovering lower percentages of losses over time, hence select developed ratios"

Adv of Ratio approach

• Less leveraged than development, which is based on S&S dollars
• Produces ratios of \(\dfrac{\text{Ult S\&S}}{\text{Ult Claims}}\), a diagnostic… if this ratio for any particular year seem unreasonable, then a more reasonable S&S ratio can be selected for that year.

Reinsurance

Unpaid claims estimates may be needed net of reinsurance basis.
- Develop net \(\triangle\) directly
- Develop gross \(\triangle\) and ceded \(\triangle\) separately \(\implies\) Estimate net

Reinsurance relationships
- QUOTA SHARE
- net claims = constant \% of gross claims
- constant % ceded by reinsurer.
- "70%" quota share. STATE YOUR ASSUMPTION, whether 70% is retained or ceded.
- Per-risk or per-occurrence Excess of Loss (XOL) treaty.
- Cede all amounts above a certain retention and up to a certain limit
- Individual claims
- STOP LOSS treaty (Aggregate XOL treaty)
- above a certain retention up to a certain limit on aggregate loss amounts for insurer's book (multiple year period)
- This applies to \(\text{Losses net- of per-risk, Gross of Stop loss}\)
- stop loss "limit" \(\to\) refers to retention. Limit is ignored.

Tail Factors

• QUOTA SHARE
  • Tail factors for gross, net & ceded are the same
  • since constant percentage
• XOL & STOP LOSS treaties
  • ceded \(\triangle\) tail factor \(\gt\) gross triangle \(\impliedby\) when retention limit is reached.
    • because all development happens in the ceded layer
  • net \(\triangle\) tail factor \(\lt\) gross triangle \(\impliedby\) retention limited reached
    • net losses may be capped by the reinsurance protection.

Misc.

• Development factors can apply to even attachment points. Spring 2014 E5 Q11
• Normally we would develop the gross and ceded triangle separately, and then come up with an estimate for the net triangle. But if the data in ceded is too thin for development, we would develop the net directly.
• A #doubt, what happens if there is downward development with a reinsurance in place? Does the reinsurance get the amount back?

Mistakes

1. Fall 2014 Exam 5 - Q21: Found dev factors for Gross, but applied them to net to get ultimate amounts. Blunder.
2. Fall 2018 Exam 5 - Q15: A good problem to test if you really understood how XOL retention limits work with transactions.
   • =min(retention_lim - prev_gross, thisCYtransaction) we are left with retention_lim - prev_gross amount that will be retained, so that becomes the limit to thisCYtransaction

---

1. "Reported" recoveries include Case O/S. "Paid" or "Received" don't. ↩