Development

GOAL: Estimate Ultimate values of premium and loss data

• Understand the environment (internal and external)
• There can be changes¹, understand them thoroughly
• Needs discussion!

Things to discuss with various departments of Insurer (CUDRI) memo

This might be more applicable to consulting actuaries

• Claims
  • how do you handle unpaid claims?
  • did your reserving process change?
• Underwriting
  • did the business composition change?
  • were there any large risks?
• Data processing/accounting
  • how do you handle claim payments?
  • what do you do in case of partial payments?
  • how accurate are your data sources?
• Ratemaking actuaries
  • why did you deviate from standard ratemaking procedures?
  • what data did you use?
  • what were the recent rate filings?
• In-house actuaries
  • can I get the copy of the actuarial study held?
  • can I get more background on why did you select this (ratio)?

todo Create a list of 3 questions to ask each executive from Friedland’s Reserving Book

Development Triangles

• See the changes in claims data over time
• age and valuation date

Let’s first query the claims database and aggregate data by accident year (the year now is 2028)

AY2024

• collect data for AY2024 in 12-month intervals
• a/o 2024-12-31 ABC paid $108M on all accidents (occurring from 2024-01-01)
  • age: 12 months
  • valuation date: 2024-12-31

Accident Year	Cumulative Paid Claims by Age ($US Millions)
	12 Months	24 Months	36 Months	48 Months
2024	108	128	144	180

We are basically looking at the claims that happened in 2024 in their respective ages.

Now, we do the same for AY2025, AY2026 and AY2027 (we have data for every year). So, we get a triangle

	12 Months	24 Months	36 Months	48 Months
2024	108	128	144	180
2025	100	121	152
2026	108	150
2027	112
`
That’s all! That’s the development triangle.

Reading the Development Triangle

• If we want to look at all claims that happened a/o a specific year, let’s say 2027, then all we need to do is read the upward sloping diagonal
  • which in this case are 112 150 152 180
  • note that these are cumulative values, so summing them up will give us the total losses a/o a 2027

Triangles that can be derived

• Incremental Paid claims:
  • Add up the CY paid for each transaction in the year
• Cumulative Paid Claims
  • Cumulatively add through a given year (from the previous result)
• Cumulative Reported Claims
  • Add Cumulative Paid claims + Year End Case Reserves
• Cumulative Reported Claim Count
  • Just count them
• Cumulative Closed Claim Count
  • Just invert it…

We can also perform Diagnostics using Development Triangles

Developing Premiums

When to develop premiums?

• Incomplete year of data is used: (for Policy Year Analysis)
  • Balance Responsiveness and Stability
  • written policy year takes longer to close
  • premium data for active policies have to be developed to ultimate²
  • Method: Study the historical pattern of premiums to estimate mid-term changes or cancellations on policy year premium
• LOB with Premium Audits:
  • the actual exposure for an insured is not known at the inception of the policy
  • thus, initial premium is charged then based on estimated exposure
  • once actual exposure is known, premium is adjusted

Historical Patterns depend on several factors

doubt

1. types of plans available from insurer
2. internal company policies
3. stability of historical relationship b/w estimated premium and audited premium.

Calendar Year Data

• Premium development generally won’t be necessary
• Data at the end of CY is final.
• If audit patterns change, premium development on CY data can be justified.

Chain Ladder Method

Footnotes

1. class of business written, policy provisions, claims management philosophy, social and economic environment ↩

2. for newly written policies, the initial premium value is known but this value is subject to change do to a variety of reasons

   • changes in policy
   • cancellations in policy
   ↩