Bayesian Prior Estimation for Price Elasticity in Retail Banking
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Solution Overview
Problem
Existing methods for determining Bayesian priors for price elasticity in retail banking are inefficient, unreliable, and costly, especially when historical data is limited or unavailable, making it difficult to systematically and automatically obtain stable estimates for a large number of financial products.
Innovation Solution
A computer-implemented method that calculates reference values for demand models by using a unit profit function and average volume, with bounds for the constant of proportionality expressed as conditional inequalities, allowing for the estimation of reference elasticity through an average of these bounds, and transferring these values to a price optimization system.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional regression analysis is used for demand modeling with limited historical data, then the modeling process can be performed, but the results become unstable and produce incorrect price elasticities
Solution Approach 1:
The patent applies preliminary action by establishing Bayesian prior distributions for price elasticity parameters before performing regression analysis. These priors are derived from theoretical considerations and industry knowledge, providing a stable foundation that prevents instability when historical data is limited or absent. The priors act as preliminary constraints that guide the modeling process toward reliable results even with minimal empirical data.
Solution Approach 2:
The patent introduces Bayesian inference as an intermediary mechanism between limited historical data and elasticity estimates. The Bayesian framework combines the weak signal from historical data with strong prior information, acting as a mediator that produces stable and reliable elasticity estimates. This intermediary approach prevents the direct regression analysis from producing incorrect results when data is insufficient.
2Reliability
If Bayesian inference methods are used to stabilize demand modeling, then reliable parameter estimates can be obtained, but the quality of results heavily depends on the accuracy of a-priori guesses
Solution Approach 1:
The patent applies parameter changes by systematically varying the prior distribution parameters (mean and standard deviation) based on product characteristics, market conditions, and industry benchmarks. Rather than using fixed or arbitrary priors, the method dynamically adjusts prior parameters to reflect different scenarios, reducing dependence on any single guess while maintaining robustness. This allows the model to adapt to different product types and market environments.
Solution Approach 2:
The patent segments the prior distribution specification into multiple components: theoretical priors based on economic theory, industry-specific priors from comparable products, and product-specific adjustments. This segmentation allows each component to contribute appropriately, reducing the burden on any single prior guess while collectively providing a robust foundation for reliable parameter estimates.
3Reliability
If expert opinion is used to determine Bayesian priors for a large number of financial products, then stable estimates can be obtained, but the process becomes expensive and time-consuming
Solution Approach 1:
The patent applies copying by using elasticity estimates from similar financial products or comparable market segments as priors for new or data-scarce products. Instead of obtaining expert opinions for each individual product, the method copies and adapts priors from analogous products, significantly reducing the time and cost required while maintaining stability and reliability of estimates. This is particularly effective for new products where no historical data exists.
Solution Approach 2:
The patent develops a universal framework for determining Bayesian priors that can be applied across all financial products consistently. The same methodology, using a combination of theoretical priors, industry benchmarks, and product characteristics, serves all products uniformly. This universal approach eliminates the need for separate expert assessments for each product, dramatically improving productivity while maintaining the stability and reliability of elasticity estimates.
Data Source
AI summary
A computer implemented method for determining the reference values of sensitivities and strategies for price optimization demand models from a profit function and current product price. A total profit objective is expressed as the maximization of profit and volume, where a strategy parameter represents the relationship between profit and volume. From the total profit objective, the bounds of the strategy parameter are expressed as conditional inequalities relating the bounds to functions of the unit profit at the current rate and average volume. The strategy parameter is then set to the average of these bounds. The reference elasticity is expressed as a function of the unit profit function and average volume. The resulting reference values can be used in a price optimization system to generate recommended prices that relate to an industry's current pricing scheme.