MARGINAL PRICING: AN EDUCATIONAL MODEL TO PRICE CORRELATED RISKS IN INSURANCE

Open Access
Author:
Callahan, Michael G
Area of Honors:
Mathematics
Degree:
Bachelor of Science
Document Type:
Thesis
Thesis Supervisors:
  • Nan Zhu, Thesis Supervisor
  • Dennis Keith Pearl, Honors Advisor
Keywords:
  • actuarial science
  • mathematics
  • stochastic
  • monte carlo
  • insurance
  • finance
  • simulation
  • pricing model
Abstract:
This paper expands upon existing educational actuarial models to construct a new general insurance pricing model that will demonstrate the effects of additional actuarial concepts to students via an interactive web application built in R-Shiny. The new model is designed to calculate the marginal cost of adding one additional policy, or group of policies, to an existing business portfolio of policies. The paper achieves this by viewing all policies from an investment portfolio perspective and projecting the resulting cashflows forward in time using simulation. Then, the model assesses the simulation and calculates the average net present value (NPV) of the simulation, which is the sole financial objective for the company represented by the model. The paper defines the “fair upfront marginal premium” of a given policy to be the change in average NPV caused by adding the additional policy. Thus, the premium can be considered the upfront premium rate at which the insurer’s utility is the same with the additional insured as without. The resulting model is a simplification of the different actuarial measurements taken to effectively price insurance in industry, but serves as an apt educational framework for students to understand more practical business applications. Particularly, the key advantage of the model is in revealing deeper patterns with respect to the cost of policy loss variance. Ultimately, this paper finds that under such a pricing framework, the risk appetite of an insurance company varies dramatically depending upon its current financial circumstance, and that this model can provide revealing metrics of implied risk premiums to provide objective measures of risk appetite.