# P&C Loss Reserving Valuation Methods

In Property and Casualty insurance, also known as P&C insurance, we use 3 main methods to value reserves.

Contents

## P&C Loss Reserving

Why do we need to value reserves and what is a reserve?
In a typical business such as a hotdog stand, companies known how much profit they make when they sell a product. The hotdog stand owner knows how much his costs are. This comprises of rent, cost of materials, and other expenses which are typically all known. Therefore he knows his profits.
For insurance companies, you don’t know how much profit you make until further down the road. For example, when you buy a car insurance policy, the insurance company knows how much revenue it makes (the premiums you pay) but doesn’t know how much the cost is (how much they will pay out to you) because the accidents haven’t happened yet. For longer tail lines of business such as commercial general liability, they won’t know until many years down the road. So we have to estimate the costs in order to find out how much the final cost will be. The difference between the final cost and what’s been paid so far is called the loss reserve.

## Loss Ratio Method

Also known as Expected Claims Ratio method
This actuarial valuation method is the simplest and is often used when there’s little experience (claims history) in the line of the business (LOB) or the experience is subject to change. It allows the actuary to assign an arbitrary loss ratio multiplied by the earned premiums to arrive at an ultimate loss figure.
Ultimate Losses = Earned Premium * Loss Ratio
IBNR = Ultimate Losses – Incurred Losses = Earned Premium * Loss Ratio – Incurred Losses

## Chain Ladder Method

Also known as the Loss Development Method
The Chain Ladder Method assumes that past experience is an indicator of future experience, meaning that the past data is a good indicator for what happens in the future. This method is used often for stable lines of business. Loss development patterns in the past are used to estimate how claim amounts will increase (or decrease) in the future. The explanation is a bit lengthy and will go into its own article.

## Bornhuetter Ferguson

This valuation method is a combination of the loss ratio method and the chain ladder method. It can be used on reported or on paid losses. Recall that the final paid should be the same as the final reported.
Let w be the weight to assign to the chain ladder method.
Then
Ultimate Losses = (Incurred Losses)*(Cumulative Loss Development Factor)*w + (Expected Loss Ratio)*(Exposure Base)*(1-w)
=(Chain Ladder Method Ultimate)*w+(Loss Ratio Method Ultimate)*(1-w)
As you can see, it’s a weighted average between the loss ratio method and the chain ladder method.

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