# In profit testing, why do we assume an initial reserve of 0 if E(L0) is not equal to zero?

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Ie. why is 0V = 0 in all our profit testing tables if that is not the policy value at time 0?

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There are various reasons why insurers undertake a profit testing exercise, for example to set premiums and reserves so as to assess the profitability of a product. This is usually done on a best estimate basis to get a realistic idea of how the product will perform.

Recall that technically policy values and reserves are not the same thing. Policy values are the assets required to meet the expected future payments to policyholders under a particular basis (usually calculated using a prudent basis). The reason there might be a shortfall  between premiums the company receives and the expected benefits the company is obligated to pay is that the expected cost of paying the benefit generally increases over the term of the contract whereas the premiums to fund these benefits are usually level.

Reserves, on the other hand, are what insurers actually holds in order to meet the expected future benefits and expenses. These may be more or less (if regulation permits) than the policy values. In practice the regulator usually prescribes how the reserves should be calculated depending on the type of product and a whole slew of other factors.

In profit testing the reason why reserve are not set up when the policy is issued (i.e. why $${}_0V = 0$$)

1. The product should be priced such that the premiums received are sufficient to meet all expected future benefits and expenses and contribution to profits for proprietary insurance companies, hence no need for reserves at this point. If this is not the case then this is a sign of bad product design.
2. Insurance companies are required by regulation to do valuations at least once a year. Most insurance companies will do valuations at year end and given the point above it is at this time that the premiums may then start to be insufficient to meet the cost of the future benefits and expenses.
3. Most policyholders that lapse their policies tend to lapse in the first year and hence the reserves that the insurer would have set up for these policyholders should be released. By holding reserves for these policyholders the insurer might tie up a large amount of capital that might be used better elsewhere in the business. This is one of the reason why insurers have a lapse assumption embedded in their pricing models.
4. There is a cost to capital and generally companies do not want to tie up large sums of money for a prolonged period of time. So if they can, they will generally want to set up as little reserves as possible as late as possible.

All that being said, there are cases when an insurance company might actually hold reserves at inception. Refer here for a case when this can occur.