Recent changes in frequency have also complicated the selection of an appropriate severity trend. Both our internal and consulting actuaries have observed fluctuating but generally lower claims frequency that cannot be attributed to any single factor. We believe that much of the reduction in the number of claims is the result of a decline in the filing of frivolous lawsuits that have historically been dismissed or otherwise result in no payment of indemnity on the part of our insureds. With fewer frivolous claims being filed we expect that the claims that are filed have the potential for greater average losses, or greater severity. As a result, we cannot be certain as to the impact this decline will ultimately have on the average cost of claims. Based on a weighted average of payments, resolution of 85% of claims for a given accident year requires more than eight years (based on a weighted average of payments). Due to this long tail, it will be several years before we are able to determine if the decline in frequency has indeed resulted in a related increase in severity.
Our receivable from reinsurers on unpaid losses and loss adjustment expenses represents our estimate of the amount of our reserve for losses that will be recoverable under our reinsurance programs. We base our estimate of funds recoverable upon our expectation of ultimate losses and the portion of those losses that we estimate to be allocable to reinsurers based upon the terms of our reinsurance agreements. Our assessment of the collectability of the recorded amounts receivable from reinsurers considers the payment history of the reinsurer, publicly available financial and rating agency data, our interpretation of the underlying contracts and policies, and responses by reinsurers.
When a pricing service does not provide a value for one of our fixed maturity securities, management estimates fair value using either a single non-binding broker quote or pricing models that utilize market based assumptions which have limited observable inputs. The process involves significant judgment in selecting the appropriate data and modeling techniques to use in the valuation process. For disclosure purposes we classify fixed maturity securities that are valued using limited observable inputs as Level 3 securities.
The acquisition of APS contributed gross, ceded and net premiums written during the years ended December 31, 2011 and 2010 as follows:
We similarly reduced our estimates of the premium due to reinsurers by $30.6 million and $13.4 million in 2011 and 2010, respectively, because the premium due to reinsurers is based in part on amounts recovered.
Termination of a captive insurance arrangement, managed by ProAssurance, increased 2010 underwriting expense by $2.6 million. There was no similar transaction in 2011.
(3) A partial redemption of our BOLI increased tax expense in 2010 by approximately $1.3 million; there were no BOLI redemptions during 2011.
Our non-physician healthcare providers are primarily dentists, chiropractors, optometrists, and allied health professionals. The 2010 increase is primarily related to allied health coverages, but also includes additional premium of $1.2 million generated by a targeted marketing campaign to optometrists.