Integrating Deterministic and Probabilistic Reserves

Abstract

Summary Probabilistic reserves evaluation offers the opportunity to describe a reserves volume in terms of the specific statistical certainty associated with that volume, as opposed to relying on the definitions associated with deterministic reserve classifications. Where a reserves entity has volumes identified for two or more certainty levels, knowledge of the reserves distribution may be used to interpolate reserve volumes at other certainty levels. This interpolation forms the basis of statistical reserves aggregation. Assignment of confidence levels to the deterministic categories of Proved or Probable supports both deterministic and probabilistic reporting. This paper examines the mechanisms which control the shape of the reserves distribution curve; demonstrates the applicability of normal distribution curves to reserves distributions; and outlines a procedure for statistical reserves aggregation which may coexist with deterministic aggregation. Introduction Traditionally, when reserves are aggregated for reporting purposes, the deterministic approach is used. This involves the arithmetic addition of reserve volumes for each reserve category being reported on. With the increasing use of statistical methods in reserves determination, the arithmetic method may not always be appropriate.1 This paper reviews the implications of using statistics, and demonstrates their applicability in reserves assessment. In order to facilitate traditional reserves reporting, the approach described relies on assigning confidence levels to existing reserve categories, to support both deterministic and probabilistic reporting. Probabilistic reserves aggregation offers an opportunity to more accurately classify and report on reserve volumes, though there are elements of probabilistic aggregation that may appear counter intuitive. Understanding the results of a probabilistic aggregation involves understanding the underlying statistical principles involved. Normal Distribution and Statistical Aggregation The simplest distribution pattern is a flat distribution, such as the outcome from rolling a single die. Each side of a single die is equally likely to come up when rolled. When more than one die is rolled though, the sum of two or more dice will more closely approximate a normal distribution pattern. Normal distribution patterns occur when multiple independent variables act in a cumulative fashion with a common outcome. To understand the effect of adding together normally distributed outcomes, consider a pair of dice being rolled. Six sides on each die give thirty-six possible combinations, though most of these are not unique. Table 1 displays both the distinct outcomes, as well as the frequency of occurrence. The third column lists the cumulative frequency, which is the likelihood that any roll of two dice will result in a value equal to or greater than the one being considered. Thus there are six chances out of thirty-six of getting a value of ten or greater. Dividing the cumulative frequency of each outcome by thirty-six yields the cumulative probability of each outcome. This is often shown graphically as an "S" shaped cumulative probability - curve Fig 1. The probability for each value includes the probability for that value added to the sum of the probabilities of higher values.