Description: This is a presentation From 38th Annual Actuarial Research Conference 8/9/2003, University of Michigan, Ann Arbor, Michigan. Pricing health insurance presents numerous statistical problems. This paper develops a non-parametric method for handling these problems. This method involves kernel density estimation of the charge level distribution and also kernel smoothing between the reimbursement function derivatives. It derives some properties of the estimates so obtained. It illustrates the method with some dental data and compares the results to some other simpler estimation techniques.