Aggregate implements an efficient fast Fourier transform (FFT)-based algorithm to approximate compound probability distributions. Leveraging FFT-based methods offers advantages over recursion and simulation-based approaches, providing speed and accuracy to otherwise time-consuming calculations. Combining user-friendly features and an expressive domain-specific language called DecL, Aggregate enables practitioners and nonprogrammers to work with complex distributions effortlessly. The software verifies the accuracy of its FFT-based numerical approximations by comparing their first three moments to those calculated analytically from the specified frequency and severity. This moment-based validation, combined with carefully chosen default parameters, allows users without in-depth knowledge of the underlying algorithm to be confident in the results. Aggregate supports a wide range of frequency and severity distributions, policy limits and deductibles, and reinsurance structures and has applications in pricing, reserving, risk management, teaching, and research. It is written in Python.

In this paper, we provide a theoretical framework justifying the existence of a correlation risk premium in a market with two traded assets. We prove that risk-neutral dependence can differ substantially from real-world dependence by characterizing the set of risk-neutral martingale measures. This implies that implied correlation can be significantly different with the realized correlation. Depending on the choice of the market regarding the pricing measure, implied correlation can be high or low. We label the difference between risk-neutral and real-world correlation the “correlation gap” and make the connection with correlation risk premium. We show how dispersion trading can be used to exploit this correlation gap and demonstrate how there can exist a negative correlation risk premium in the financial market.

We study a discrete-time life cycle retirement planning problem for individual workers with four distinct investment options: self-management with dynamic investment (S), self-management with benchmark investment (B), hire-management with flexible allocation ($\text{H}_{1}$), and hire-management with alpha focus ($\text{H}_{2}$). We examine the investment strategies and consumption patterns during the defined contribution fund accumulation period, ending with a life annuity purchase at retirement to finance post-retirement consumption. Based on the calibrated model using US data, we employ numerical dynamic programming technique to optimize worker’s financial decisions. Our analysis reveals that, despite the agency risk, delegated investments can add value to a worker’s lifetime utility, with the $\text{H}_2$ option yielding the best lifetime utility outcome. However, after taking the fund management fee into consideration, we find that both the $\text{H}_1$ and $\text{H}_2$ options may not offer additional value compared to the S option, yet they still surpass the B option in performance.

The association between economic variables and the frequency and duration of disability income insurance (DII) claims is well established. Across many jurisdictions, heightened levels of unemployment have been associated with both a higher incidence and a longer duration of DII claims. This motivated us to derive an asset portfolio for which the total asset value moves in line with the level of unemployment, thus, providing a natural match for the DII portfolio liabilities. To achieve this, we develop an economic tracking portfolio where the asset weights in the portfolio are chosen so that the portfolio value changes in a way that reflects, as closely as possible, the level of unemployment. To the best of our knowledge, this is the first paper applying economic tracking portfolios to hedge economic risk in DII. The methodology put forward to establish this asset-liability matching portfolio is illustrated using DII data from the UK between 2004 and 2016. The benefits of our approach for claims reserving in DII portfolios are illustrated using a simulation study.

Many pension plans and private retirement products contain annuity factors, converting the funds at some future time into lifelong income. In general model settings like, for example, the Li-Lee mortality model, analytical values for the annuity factors are not available and one has to rely on numerical techniques. Their computation typically requires nested simulations as they depend on the interest rate level and the mortality tables at the time of retirement. We exploit the flexibility and efficiency of feed-forward neural networks (NNs) to value the annuity factors at the time of retirement. In a numerical study, we compare our deep learning approach to (least-squares) Monte-Carlo, which can be represented as a special case of the NN.

We consider a new approach in the definition of two-dimensional heavy-tailed distributions. Specifically, we introduce the classes of two-dimensional long-tailed, of two-dimensional dominatedly varying, and of two-dimensional consistently varying distributions. Next, we define the closure property with respect to two-dimensional convolution and to joint max-sum equivalence in order to study whether they are satisfied by these classes. Further, we examine the joint-tail behavior of two random sums, under generalized tail asymptotic independence. Afterward, we study the closure property under scalar product and two-dimensional product convolution, and by these results, we extended our main result in the case of jointly randomly weighted sums. Our results contained some applications where we establish the asymptotic expression of the ruin probability in a two-dimensional discrete-time risk model.

This paper utilizes neural networks (NNs) for cycle detection in the insurance industry. The efficacy of NNs is compared on simulated data to the standard methods used in the underwriting cycles literature. The results show that NN models perform well in detecting cycles even in the presence of outliers and structural breaks. The methodology is applied to a granular data set of prices per risk profile from the Brazilian insurance industry.

Healthcare costs tend to increase with age. In particular, in the case of illness, the last year before death can be an exceptionally costly period as the need for healthcare increases. Using a novel private insurance dataset containing over one million records of claims submitted by individuals to their health insurance providers during the last year of life, our research seeks to shed light on the costs before death in Switzerland. Our work documents how spending patterns change with proximity to dying. We use machine learning algorithms to identify and quantify the key effects that drive a person’s spending during this critical period. Our findings provide a more profound understanding of the costs associated with hospitalization before death, the role of age, and the variation in costs based on the services, including care services, which individuals require.