Geology and Mining: Mineral Resources and Reserves: Their Estimation, Use, and Abuse

Editor’s note: The Geology and Mining series, edited by Dan Wood and Jeffrey Hedenquist, is designed to introduce early-career professionals and students to a variety of topics in mineral exploration, development, and mining, in order to provide insight into the many ways in which geoscientists contribute to the mineral industry. Abstract Resource and reserve estimation is a critical step in mine development and the progression from mineral exploration to commodity production. The data inputs typically change over time and reflect variations in geoscientific knowledge as well as the modifying factors required by regulation for estimating a reserve. These factors include mineral (ore) processing, metallurgical treatment of the ore, infrastructure requirements for mine and workforce, and the transportation of processed products to buyers; others that will affect the production of metals and/or minerals from a deposit include economic, marketing, legal, environmental, social, and governmental factors. All are needed by the mining industry to quantify the contained mineralization within mineral deposits that likely warrant the significant capital investment required to build a mine. However, these resource and reserve data are estimates that change over time due to unpredicted variations in the initial inputs. Paramount to the two estimates are the quality and accuracy of the geologic inputs and the communication of these to the professionals tasked with making each estimate. Geostatistical processing of the grade of the resource has become a dominant element of the estimation process, but this requires transparent and informed communication between geologists and mining engineers with the geostatistician responsible for mathematically processing the grade data. Regulatory constraints also mean that estimated resources and reserves seldom capture the full extent of a mineral deposit. Similarly, co- and by-product metals and minerals that are commonly produced by mines may not be captured by resource and reserve estimates because of their limited economic contribution. This suggests that reporting standards for co- and by-products—particularly for the critical metals that may have a sharp increase in demand—need improvement. Finally, the importance of these data to the mining industry is such that informing investors and the broader public about the nature of resource and reserve estimates, and the meaning of associated terminology, is also essential when considering the global metal and mineral supply, and the role of mining in modern society.

A GAMMA MOVING AVERAGE PROCESS FOR MODELLING DEPENDENCE ACROSS DEVELOPMENT YEARS IN RUN-OFF TRIANGLES

ABSTRACT We propose a stochastic model for claims reserving that captures dependence along development years within a single triangle. This dependence is based on a gamma process with a moving average form of order $p \ge 0$ which is achieved through the use of poisson latent variables. We carry out Bayesian inference on model parameters and borrow strength across several triangles, coming from different lines of businesses or companies, through the use of hierarchical priors. We carry out a simulation study as well as a real data analysis. Results show that reserve estimates, for the real data set studied, are more accurate with our gamma dependence model as compared to the benchmark over-dispersed poisson that assumes independence.

Claim Watching and Individual Claims Reserving Using Classification and Regression Trees

We present an approach to individual claims reserving and claim watching in general insurance based on classification and regression trees (CART). We propose a compound model consisting of a frequency section, for the prediction of events concerning reported claims, and a severity section, for the prediction of paid and reserved amounts. The formal structure of the model is based on a set of probabilistic assumptions which allow the provision of sound statistical meaning to the results provided by the CART algorithms. The multiperiod predictions required for claims reserving estimations are obtained by compounding one-period predictions through a simulation procedure. The resulting dynamic model allows the joint modeling of the case reserves, which usually yields useful predictive information. The model also allows predictions under a double-claim regime, i.e., when two different types of compensation can be required by the same claim. Several explicit numerical examples are provided using motor insurance data. For a large claims portfolio we derive an aggregate reserve estimate obtained as the sum of individual reserve estimates and we compare the result with the classical chain-ladder estimate. Backtesting exercises are also proposed concerning event predictions and claim-reserve estimates.

Property-Liability Insurers’ Discretionary and Nondiscretionary Loss Reserve Error: Relation with Investor Sentiment

We examine whether investor sentiment is associated with loss reserve estimates of property-liability (P/L) insurers. Using the Michigan Consumer Confidence Index as a proxy for sentiment, we find that the level of investor sentiment is negatively associated with discretionary component of loss reserve error. In contrast, our evidence does not suggest a similar relationship hold for investor sentiment and nondiscretionary loss reserve error. Further analysis indicates that stock insurers are more sensitive to investor sentiment than mutual insurers, in terms of discretionary component of loss reserves. The results are consistent with our hypothesis that P/L insurers cater to investors’ optimism (pessimism), driven by investor sentiment, via discretionary loss reserve claims. For robust test, we also measure investor sentiment by using two alternative proxies: the Conference Board Consumer Confidence Index, and the index in the stock market developed by Baker and Wurgler (2006, 2007). The results are consistent. Our study discovers a new rationale for why insurers may use discretion over their loss reserves.

Hydrocarbon prospectively determination of “eagle field”, coastal swamp ii Niger delta.

Seismic and well log data were collected from onshore depobelt of Nigeria with a total of 1000 seismic lines and 3 wells. The main objective of the study was to determine hydrocarbon prospectivity and reserve estimates of the field. The evaluation centred on seismic interpretation and 3D visualisation (DHI detection) of the “Ejanla Field” 3D in total, Four horizons have been interpreted regionally for correlation purposes and three as prospect specific horizons. Four prospects and some, more speculative leads were identified in the area of which most are conventional three way dip/fault closures and some hanging wall closures. The potential for stratigraphic trapping was also recognized. The study showed that the small closure areas and limited hydrocarbon column lengths affected the number of prospects and at the shallow levels.The main risk to oil prospectivity in the area as revelled by the data interpretation is gas which may have resulted from the observed higher geothermal gradient in the deeper depth. Reservoir development and retention (overpressure) for prospects and leads in the deeper and more distal sedimentological settings form additional risks.

A Robust General Multivariate Chain Ladder Method

The chain ladder method is a popular technique to estimate the future reserves needed to handle claims that are not fully settled. Since the predictions of the aggregate portfolio (consisting of different subportfolios) do not need to be equal to the sum of the predictions of the subportfolios, a general multivariate chain ladder (GMCL) method has already been proposed. However, the GMCL method is based on the seemingly unrelated regression (SUR) technique which makes it very sensitive to outliers. To address this issue, we propose a robust alternative that estimates the SUR parameters in a more outlier resistant way. With the robust methodology it is possible to automatically flag the claims with a significantly large influence on the reserve estimates. We introduce a simulation design to generate artificial multivariate run-off triangles based on the GMCL model and illustrate the importance of taking into account contemporaneous correlations and structural connections between the run-off triangles. By adding contamination to these artificial datasets, the sensitivity of the traditional GMCL method and the good performance of the robust GMCL method is shown. From the analysis of a portfolio from practice it is clear that the robust GMCL method can provide better insight in the structure of the data.