Relevant applications of Monte Carlo simulation in Solvency II

Abstract

The definition of solvency for insurance companies, within the European Union, is currently being revised as part of Solvency II Directive. The new definition induces revolutionary changes in the logic of control and expands the responsibilities in business management. The rationale of the fundamental measures of the Directive cannot be understood without reference to probability distribution functions. Many insurers are struggling with the realisation of a so-called “internal model” to assess risks and determine the overall solvency needs, as requested by the Directive. The quantitative assessment of the solvency position of an insurer relies on Monte Carlo simulation, in particular on nested Monte Carlo simulation that produces very hard computational and technological problems to deal with. In this paper, we address methodological and computational issues of an “internal model” designing a tractable formulation of the very complex expectations resulting from the “market-consistent” valuation of fundamental measures, such as Technical Provisions, Solvency Capital Requirement and Probability Distribution Forecast, in the solvency assessment of life insurance companies. We illustrate the software and technological solutions adopted to integrate the Disar system—an asset–liability computational system for monitoring life insurance policies—in advanced computing environments, thus meeting the demand for high computing performance that makes feasible the calculation process of the solvency measures covered by the Directive

Machine Learning-Based Elastic Cloud Resource Provisioning in the Solvency II Framework

“…The Dynamic Investment Strategy with Accounting Rules (DISAR) System [9], [8] is designed for the evaluation and control of minimum-guaranteed profit-sharing life policies indexed to the returns of dedicated funds (segregated funds). It is based on market-consistent evaluation criteria under uncertainty in a general asset-liability management (ALM) framework.…”

Machine learning techniques in nested stochastic simulations for life insurance

“…By definition, the expectation under the risk‐neutral measures accounts for the market price of risk that investors assign to (risky) contingent claims. Being computationally very efficient, the Monte Carlo technique is used for the evaluation of the expectation (typically, an integral) whenever closed form solutions are not available, or the dimension of the random process is not sufficiently small 2 to use quadrature techniques.…”

“…At present, given the number of life insurance contracts to be evaluated, the complexity of their payoffs, the large number of risk drivers and the availability of computing power, the nested Monte Carlo approach cannot be pursued by brute force , 2 at least in computing times suited for the management of the insurance companies (even with high‐level commercial cloud solutions of several hundreds of processors). Therefore, different strategies have been proposed in the literature in order to reduce the computational burden.…”

“…In order to have a good estimation of the SCR , both the number of risk‐neutral and real‐world simulations have to be very large, thus resulting in a “compute‐intensive” process 2,18,19 . Nevertheless, nested Monte Carlo simulation is the standard approach for insurance undertakings 3,4,17 even if it can present prohibitive computational challenges.…”

“…At present, to achieve this trade‐off, the insurance undertakings mainly use high performance computing technology (parallel and distributed systems, grid computing, cloud computing) 2 and LSMC method 21…”