Abstract We introduce $${\text {\texttt {openIRM}}}$$ , the Internal Risk Model of an artificial life insurer, designed to allow an easy benchmarking of nested simulation techniques for Solvency Capital Requirement ( $${{\,\textrm{SCR}\,}}$$ ) estimation under Solvency II and other actuarial methods. $${\text {\texttt {openIRM}}}$$ integrates an economic scenario generator and a cash flow projection model, enabling the computation of the available capital (basic own funds) through both the direct and indirect method. Leveraging a two-factor Gaussian model for stochastic short rates and a generalized Black-Scholes model for stock dynamics, the framework supports policyholder investments via guaranteed minimum-income benefit contracts. We extend the asset-liability management model by Diehl et al. (EAJ 13(1), 2022), and prove the theoretical convergence of the direct and indirect method under appropriate assumptions. Calibrated using interest rate caps from 2016 to the end of 2023, $${\text {\texttt {openIRM}}}$$ allows estimation of available capital distributions and $${{\,\textrm{SCR}\,}}$$ dynamics for each trading day in that range. The source code of $${\text {\texttt {openIRM}}}$$ written in is publicly available on at https://gitlab.cc-asp.fraunhofer.de/itwm-fm-lv-public/openirm . We also provide standalone executables that, after installation, can be accessed via the command line interface or with the provided wrappers in , and .

Abstract If individuals at the highest mortality risk are also least likely to lapse a life insurance policy, then lapse-supported premiums magnify adverse selection costs. As an example, we model ‘Term to 100’ contracts, and risk as revealed by genetic test results. We identify three methods of managing lapse surplus: eliminating it by design; disposing of it retrospectively (through participation); or disposing of it prospectively (through lapse-supported premiums). We then assume a heterogeneous population in which: (a) insurers cannot identify individuals at high mortality risk; (b) a secondary market exists that prevents high-risk policies from lapsing; (c) financial underwriting is lax or absent; and (d) life insurance policies may even be initiated by third parties as a financial investment (STOLI). Adverse selection losses under (a) are typically very small, but under (b) can be increased by multiples, and under (c) and (d) increased almost without limit. We note that the different approaches to modeling lapses used in studies of adverse selection and genetic testing appear to be broadly equivalent and robust.

Abstract If a health insurance product has only few insured, its claims experience becomes very volatile and is therefore not reliable enough as the only source for repricing the product. Traditionally, a similar product with many insured is used as a reference. However, legislative changes and market forces have led to a fragmentation of products. As a result, such a reference product with many insured is often no longer available. Here we propose a statistical model that combines the data of several products with few insured to derive a common relative claim inflation as well as the expected claims of these products in the future, thus enabling stable pricing for these products. The model was designed so that the usual premium adjustment process is changed as little as possible, making it easy to use in practice.

Abstract Random delays between the occurrence of accident events and the corresponding reporting times of insurance claims is a standard feature of insurance data. The time lag between the reporting and the processing of a claim depends on whether the claim can be processed without delay as it arrives or whether it remains unprocessed for some time because of temporarily insufficient processing capacity that is shared between all incoming claims. We aim to explain and analyze the nature of processing delays and build-up of backlogs. Development patterns for incoming reported claims that form the basis for claims reserving may be distorted by backlogs when transformed into processed (or paid) claims. In a first step, we show how to infer hidden development patterns from processed claims data. In a second step, we discuss how backlogs impact claims costs, and we show how to select processing capacity optimally in order to minimize claims costs, taking delay-adjusted costs and fixed costs for claims settlement capacity into account. Theoretical results are combined with a large-scale numerical study that demonstrates practical usefulness of our proposal.

Abstract We consider the optimal investment problem under sustainability requirements stated in [7], but solve it explicitly for the wider class of power utility functions. Further, we introduce a type of equilibrium framework that consists of modifications of the market coefficients such that the unconstrained optimal portfolio process will already satisfy the sustainability constraint. We call this modification sustainable taxation as it indicates possible taxation activities by the state to steer investors towards sustainable assets.