2019/07/02 by Yuqing Zhang, Zhang, Yuqing, Neil Walton +1 · 1 citation
Computer Science · Decision Sciences · Energy · #Gaussian Processes and Bayesian Inference #demographic modeling and climate adaptation #Energy, Environment, and Transportation Policies
paper · pdf · doi:10.48550/arxiv.1907.05381
We study the application of dynamic pricing to insurance. We view this as an\nonline revenue management problem where the insurance company looks to set\nprices to optimize the long-run revenue from selling a new insurance product.\nWe develop two pricing models: an adaptive Generalized Linear Model (GLM) and\nan adaptive Gaussian Process (GP) regression model. Both balance between\nexploration, where we choose prices in order to learn the distribution of\ndemands & claims for the insurance product, and exploitation, where we\nmyopically choose the best price from the information gathered so far. The\nperformance of the pricing policies is measured in terms of regret: the\nexpected revenue loss caused by not using the optimal price. As is commonplace\nin insurance, we model demand and claims by GLMs. In our adaptive GLM design,\nwe use the maximum quasi-likelihood estimation (MQLE) to estimate the unknown\nparameters. We show that, if prices are chosen with suitably decreasing\nvariability, the MQLE parameters eventually exist and converge to the correct\nvalues, which in turn implies that the sequence of chosen prices will also\nconverge to the optimal price. In the adaptive GP regression model, we sample\ndemand and claims from Gaussian Processes and then choose selling prices by the\nupper confidence bound rule. We also analyze these GLM and GP pricing\nalgorithms with delayed claims. Although similar results exist in other\ndomains, this is among the first works to consider dynamic pricing problems in\nthe field of insurance. We also believe this is the first work to consider\nGaussian Process regression in the context of insurance pricing. These initial\nfindings suggest that online machine learning algorithms could be a fruitful\narea of future investigation and application in insurance.\n