Bayesian Modelling, Monte Carlo Sampling and Capital Allocation of Insurance Risks

Abstract

Abstract: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 to calculate capital allocations for a general insurance company is developed, with a focus on coherent capital allocation that is compliant with the Swiss Solvency Test. The data used is based on the balance sheet of a representative stylized company. For each line of business in that company, allocations are calculated for the one-year risk with dependencies based on correlations given by the Swiss Solvency Test. Two different approaches for dealing with parameter uncertainty are discussed and simulation algorithms based on (pseudo-marginal) Sequential Monte Carlo algorithms are described and their efficiency is analysed.

Estimation of value-at-risk for conduct risk losses using pseudo-marginal Markov chain Monte Carlo

“…The task is similar to the problem tackled in this paper, as they both involve a partition of a total amount (in our case, it is a partition of the largest operational risk loss). The difference is that in Peters et al (2017) the number of partitions is known in advance, while in ours it is not. A further similarity is that the stationary distribution sought in Peters et al (2017) is lognormal, and the PM method is used to approximate it in the MCMC process.…”

“…The difference is that in Peters et al (2017) the number of partitions is known in advance, while in ours it is not. A further similarity is that the stationary distribution sought in Peters et al (2017) is lognormal, and the PM method is used to approximate it in the MCMC process.…”

“…The context in Peters et al (2017) is the allocation of the regulatory capital of insurance companies to business units. The task is similar to the problem tackled in this paper, as they both involve a partition of a total amount (in our case, it is a partition of the largest operational risk loss).…”

Editorial: A Celebration of the Ties That Bind Us: Connections between Actuarial Science and Mathematical Finance

“…Robert J. Rietz and his group (Rietz et al (2017)) study the effect of gainsharing (via simulation) on selecting discount rates for defined benefit plans. Gareth W. Peters, Rodrigo S. Targino and Mario V. Wuthrich (Peters et al (2017)) provide a novel Monte Carlo method to calculate (coherent) capital allocations for a general insurance company. Carolyn W. Chang and Jack S. K. Chang (Chang and Chang (2017)) utilize an approach that integrates commonly used tools from actuarial science and mathematical finance to price a default-risky catastrophe reinsurance contract.…”