Case Outstanding

Case Outstanding reserving techniques project ultimate losses utilizing current case reserves (Case Outstanding) as the primary exposure base, rather than premium or historical developed losses. These techniques are often referred to as Friedland’s methods.

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Friedland’s Technique 1: Case Outstanding Development

This method projects future payments directly from the current case reserves.

Mathematical Formulation

Let $\text{OS}_t$ denote the case outstanding (case reserves) at evaluation age $t$, and let $\text{Paid}_{t, t+1}$ be the incremental paid claims between age $t$ and $t+1$.

The incremental payment ratio is calculated as:

$$\text{Payment Ratio}_{t, t+1} = \frac{\text{Incremental Paid}_{t, t+1}}{\text{Case Outstanding}_t}$$

Future incremental payments are projected by multiplying the current case outstanding by these historical ratios:

$$\text{Projected Incremental Paid}_{t, t+1} = \text{Case Outstanding}_t \times \text{Payment Ratio}_{t, t+1}$$

Appropriateness and Usage

This technique is highly appropriate in the following situations:

• Claims-Made Policies: Since there is minimal pure IBNR, case reserves represent the bulk of the outstanding liability.
• Report Year (RY) Reserving: For report year triangles where all claims are already reported, and no pure IBNR exists.
• Rapidly Reported Lines: For accident years where the vast majority of claims are reported in the first development period.
• High-Quality Case Reserving: When claims adjusters set stable, reliable case reserves that correlate closely with future payments.

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Friedland’s Technique 2: Industry CDF Leverage

Used when the insurer does not possess historical triangles but has access to the current case outstanding and industry loss development factors.

Methodology

Given the company’s current Case Outstanding ($\text{OS}$) and Paid-to-date ($\text{Paid}$), along with Industry Reported CDF ($\text{CDF}_R$) and Paid CDF ($\text{CDF}_P$):

1. Calculate the industry-implied outstanding-to-paid relationship.
2. Project company ultimate losses using: $$\text{Ultimate Losses} = \text{OS} \times \frac{\text{Industry } \text{CDF}_R}{\text{Industry } \text{CDF}_R - 1} + \text{Paid}$$

Limitations and Sensitivities

• Mismatched Profiles: Industry development patterns may not represent the specific risk profile or claim settlement practices of the subject entity.
• Large Loss Distortion: Projections are highly sensitive to case reserves set for a few large, complex claims.
• High Volatility at Early Ages: For immature years, the CDFs are highly leveraged (since $\text{CDF} - 1$ is in the denominator), leading to highly volatile ultimate estimates.
• Data Scarcity: Should only be used as a method of last resort when historical development triangles are completely unavailable.

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