Actuarial analysis of claim per payment event: theoretically developing estimation link between quantum mechanics and insurance modeling

In general, business, underwriting firms usually write policy terms by imposing additional deductible conditions in order to mitigate the risk of loss and discourage frivolous claims by modifying the indemnity payable by the underwriter where loss occurs. Under deductible conditions, underwriting firms will only be liable in a loss event where it becomes apparent that the loss has exceeded the deductible defined in the policy terms. The maximum accumulated number of losses retained by the insured applying deductible policy modifications is usually set as part of the terms and conditions of the policy documents. This paper develops an analytical framework for evaluating the effect of structural properties of dirac-delta on insurance risk variables with deductible clauses. The objective is to obtain models for the excess of loss random variable in a payment event. In order to achieve this and create analytically sound theoretical platform of investigating payment distribution functions, the quantum structure of dirac-delta is first examined in respect of probability density function. The import of adopting the dirac-delta function in this paper lies in its elegance to permit alternative technique to obtain analytically useful models for insurance severity beneficial to both the insured and insurer with particular reference to rate relativity deductible clause. We then obtained insurance excess of loss severity and variance for an arbitrary policy under deductible coverage conditions. As part of our contributions, theorems in respect of loss were stated and proved for underwriters to see reasons for their applications and use in policy underwriting decisions.