We study the optimal insurance design problem. This is a risk sharing problem between an insured and an insurer. The main novelty in this paper is that we study this optimization problem under a risk-adjusted premium calculation principle for the insurance cover. This risk-adjusted premium...

The main objective of this work is to develop a detailed step-by-step guide to the development and application of a new class of efficient Monte Carlo methods to solve practically important problems faced by insurers under the new solvency regulations. In particular, a novel Monte Carlo method...

For centuries, mathematicians and, later, statisticians, have found natural research and employment opportunities in the realm of insurance. By definition, insurance offers financial cover against unforeseen events that involve an important component of randomness, and consequently, probability...