Dynamic Pricing With Application To Insurance

Abstract

E-commerce has grown explosively in the last decade and dynamic pricing is one of the main drivers of this growth. Due to digitization and technology advances, companies are able to gather information about a product features, particularly in relation to pricing, and then dynamically improve their pricing decisions in order to maximize revenue over time. However, when a company sells a new product online, there is often little information about the demand. This thesis aims to investigate dynamic pricing with unknown demand, i.e., how can a company dynamically learn the impact of prices or other context on product demand, and simultaneously maximize long-run revenue? We first focus on the non-life insurance industry. Compared with other financial businesses, the insurance industry is relatively slow to adapt new technologies. Dynamic pricing for the insurance pricing problems has only very rarely been considered before. We consider two adaptive models for demand and claims: a generalized linear pricing model and a Gaussian process pricing model, based on the work of den Boer & Zwart (2014b), Srinivas et al. (2012) and Joulani et al. (2016). Here, neither demand or claims is known to the company. In the real world, claims are often delayed because they are only triggered when the insured events happen so are not paid out immediately when an insurance product is purchased. We first show how these methods can be applied in a simple insurance setting without any delays, and then we extend them to the setting with delayed claims. Our study shows that dynamic pricing is potentially applicable to the non-life insurance pricing problem. We then propose a simple randomized rule for the optimization of prices in revenue management with contextual information. A popular method, certainty equivalent pricing, treats parameter estimates as certain and then separately optimizes prices, but this is well-known to be sub-optimal. To overcome this problem, we advocate a different approach: pricing according to a certainty equivalent rule with a small random perturbation, and call this perturbed certainty equivalent pricing or perturbed pricing. We show that if the magnitude of the perturbation is chosen well, our new perturbed pricing performs comparably with the best pricing strategies. Furthermore, we achieve a new eigenvalue lower bound on design matrix. Finally, we study the application of reinforcement learning to the insurance pricing problem. Reinforcement learning focuses on learning how to make sequential decisions in environments with unknown dynamics and it has been successfully applied to a wide range of problems in many areas. We extend the insurance model from before to the case where the company pays dividends to shareholders and ruin probability is involved. Starting with reviewing the basics of reinforcement learning, we model the insurance pricing as a Markov decision problem and then apply reinforcement learning based techniques to solve the pricing problem. The numerical simulation shows that reinforcement learning could be a useful tool for solving pricing problems in the insurance context, where available information is limited.

Date of Award	1 Dec 2020
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Kees Van Schaik (Co Supervisor) & Neil Walton (Main Supervisor)