Loss Distribution Function for Risk Assessment
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Solution Overview
Problem
Current methods for determining the risk of losses in high excess zones are cumbersome and inaccurate, relying on extrapolation of historical data, which is time-consuming and not always representative, especially for reinsurance companies and benchmark studies.
Innovation Solution
A computer-implemented method and system that selects a loss distribution function with a cumulative distribution function and a tail characteristic associated with the line of business, fixing it to a starting excess point and fitting it to historical losses, using Convex Beta, Pareto, or Exponential distributions to accurately assess risks beyond historical data ranges.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If extrapolation of historical data is used to determine risk in high excess zones, then the method is simple to implement, but the accuracy and representativeness of risk quantification deteriorates
Solution Approach 1:
The patent applies preliminary action by pre-selecting and pre-fitting a loss distribution function to the historical data before the actual risk assessment is needed. The distribution function is fitted to historical losses up to a certain excess point, and this pre-established model is then used to assess risks in high excess zones without needing to perform complex extrapolation or data collection at the time of assessment.
Solution Approach 2:
The patent introduces a loss distribution function as an intermediary between historical data and future risk assessment. This distribution function serves as a mathematical model that bridges the gap between observed historical losses and unobserved high excess risks, allowing accurate quantification without direct observation or extensive data collection in the high excess zone.
2Measurement precision
If credibility theory methodology is applied to collect and fit data from comparable industries, then the representativeness of probability distribution improves, but the time and complexity of the process increases
Solution Approach 1:
The patent applies universality by using a single loss distribution function that can be applied across different lines of business and institutions. The Convex Beta distribution family provides a universal modeling framework that captures the essential characteristics of loss data across various contexts, eliminating the need for separate data collection and fitting processes for each specific case.
Solution Approach 2:
The patent uses parameter changes by allowing the parameters of the loss distribution function to be adjusted based on the specific characteristics of different lines of business and historical data. The Convex Beta distribution has parameters that can be calibrated to match observed data patterns, providing both accuracy and efficiency without requiring extensive data collection.
3Productivity
If conventional extrapolation methods are used, then the process is quick, but sudden jumps and discontinuities in loss distribution function occur causing unjustified price jumps
Solution Approach 1:
The patent applies inversion by reversing the conventional approach: instead of starting with historical data and attempting to extrapolate forward with methods that may produce discontinuities, the patent selects a loss distribution function with desirable mathematical properties (continuity, convexity) from the beginning and fits it to historical data. This ensures the resulting function is continuous and free of sudden jumps by construction.
Solution Approach 2:
The patent employs parameter changes by using the Convex Beta distribution family, which is parameterized to ensure continuity and convexity. By changing the parameterization approach from conventional extrapolation methods to this specific distribution family with controlled parameters, the patent achieves both speed and stability, eliminating discontinuities while maintaining computational efficiency.
Data Source
AI summary
A method and a system for determining a risk of losses, which can be implemented as a computer-implemented method and a computer system for determining for an institution the risk of losses associated with a line of business.