Using Mathematical Modeling to Study Refund Policies in Airline Pricing

Overview

Airlines have increasingly introduced flexible refund policies that allow passengers to cancel tickets and receive time-limited travel credits. These policies introduce additional uncertainty because cancellations return seat capacity and allow credits to be used for future bookings, making future demand and revenue stochastic. The airline must choose prices over time while accounting for stochastic customer arrivals and a fixed total seat capacity across the selling horizon. Under flexible refund policies, the marginal value of remaining seats depends on both future pricing decisions and uncertain credit usage, creating a recursive dynamic optimization problem. This project develops a mathematical model to analyze how flexible refund policies and credit expiration affect customer demand, optimal pricing, and airline profit. I developed a mathematical model using dynamic programming to analyze airline pricing under flexible refund and non-refundable policies. I derived customer demand functions by modeling rational purchase decisions and solving expected surplus conditions. I formulated the airline’s expected profit as a Bellman equation and used backward induction to compute optimal prices as a function of remaining seats and time. I proved theorems showing how refundability changes demand and shifts the optimal pricing function. I then implemented numerical dynamic programming and Monte Carlo simulation to evaluate pricing strategies and analyze how refundability affects airline profit, ticket sales, and customer behavior under stochastic arrivals and cancellations. The theoretical analysis shows that flexible refund policies expand customer demand and shift the optimal pricing function upward. Numerical dynamic programming and Monte Carlo simulation confirm these structural results under stochastic customer arrivals, cancellations, and credit redemption. Flexible refund policies increase airline profit by 16.5%, increase average ticket prices by 13.0%, and increase total tickets sold by 17.8% compared to non-refundable policies. Shorter credit expiration periods further increase profit by reducing future credit redemption. These results demonstrate how refundability changes optimal pricing and provide a quantitative framework for evaluating airline refund policies under uncertainty.

Competition history

• CSEF 2026 Mathematical Sciences (Senior Division) · Entry S-14-06

Related projects

Closest projects by meaning, across every fair and year in the corpus.

Browse more like this

• All Mathematics projects
• CSEF Mathematics projects
• Every CSEF 2026 project