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 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.
Highlights
Due to the new risk based solvency regulations (such as the Swiss Solvency Test FINMA (2007) and Solvency II European Comission (2009)), insurance companies must perform two core calculations
In order to fully specify the model for Credit and Surety (CY) small claims one needs to decide on the mean of the variable ZCY,s | F (t), but we postpone a detailed discussion on this point until Section 8.2, where we present the value of λCY,s
Before proceeding to the results calculated via the Sequential Monte Carlo (SMC) algorithm, in order to understand the simulated data presented in Figure 4, in Table 2 we present some results based on a “brute force” Monte Carlo simulation, which is taken as the base line for comparisons with the SMC algorithm
Summary
Due to the new risk based solvency regulations (such as the Swiss Solvency Test FINMA (2007) and Solvency II European Comission (2009)), insurance companies must perform two core calculations. The first one involves computing and setting aside the risk capital to ensure the company’s solvency and financial stability, and the second one is related to the capital allocation exercise. This exercise is a process of splitting the (economic or regulatory) capital amongst its various constituents, which could be different lines of business (LoBs), types of exposures, territories or even individual products in a portfolio of insurance policies. The amount of capital (or risk) allocated to each LoB, for example, may assist the central management’s decision to further invest in or discontinue a business line. For other allocation principles we refer the reader to Dhaene et al (2012)
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