Schedule for: 22w5119 - Emerging Insights in Insurance Statistics (Cancelled)

A buffet dinner is served daily between 5:30pm and 7:30pm in Kinnear Center 105, main floor of the Kinnear Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

A brief introduction to BIRS with important logistical information, technology instruction, and opportunity for participants to ask questions.

Insurance companies gather a growing variety of data for use in the insurance process, but most traditional ratemaking models are not designed to support them. In particular, many emerging data sources (text, images, sensors) may complement traditional data to provide better insights to predict the future losses in an insurance contract. This paper presents some of these emerging data sources and presents a unified framework for actuaries to incorporate these in existing ratemaking models. Our approach stems from representation learning, whose goal is to create representations of raw data. A useful representation will transform the original data into a dense vector space where the ultimate predictive task is simpler to model. Our paper presents methods to transform non-vectorial data into vectorial representations and provides examples for actuarial science.

By exploiting Natural Language Processing techniques we aim at grasping latent information useful for insurance to tune policy premiums. By using a large set of reports collected by the National Highway Traffic Safety Administration on accidents that occurred in the United States between 2005 and 2007, we classify medical and police reports based upon the profile of the people involved and according to the relevance of their contents. At a second step, we match these risks with the customer profiles of a company in order to add new and relevant risk covariates to improve the precision and the determination of policy premiums.

The US National Highway Traffic Safety Administration provides two databases of motor vehicle traffic accidents (MVTAs), the Crash Report Sampling System (CRSS) and the Fatality Analysis Reporting System (FARS). The CRSS database is created by sampling police-reported accidents. The FARS database is a census of MVTAs involving at least one fatality. The objective of this project is to collate the CRSS and FARS data, to construct a resource for actuarial study. The FARS database is more detailed and more complete than the GRSS database. They are combined by applying suitable weights to create a collected database that is nationally representative. We then analyse some trends and factors most pertinent to actuaries using a multinomial logistic regression. This is joint work with Carlos Araiza (PhD candidate) and Paul Marriott of the University of Waterloo.

Tree-based models have gained momentum in insurance claim loss modeling; however, the point mass at zero and the heavy tail of insurance loss distribution pose the challenge to apply conventional methods directly to claim loss modeling. With a simple illustrative dataset, we first demonstrate how the traditional tree-based algorithm's splitting function fails to cope with a large proportion of data with zero responses. To address the imbalance issue presented in such loss modeling, this paper aims to modify the traditional splitting function of Classification and Regression Tree (CART). In particular, we propose two novel actuarial modified loss functions, namely, the weighted sum of squared error and the sum of squared Canberra error. These modified loss functions impose a significant penalty on grouping observations of non-zero response with those of zero response at the splitting procedure, and thus significantly enhance their separation. Finally, we examine and compare the predictive performance of such actuarial modified tree-based models to the traditional model on synthetic datasets that imitate insurance loss. The results show that such modification leads to substantially different tree structures and improved prediction performance. Joint work with Z. Quan and W.F. Chong.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Meet in the PDC front desk for a guided tour of The Banff Centre campus.

Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo!

The occurrence of a claim often impacts not one but multiple insurance coverages provided in the contract under which the claimant is insured. To account for this multivariate feature, we propose an individual claims reserving model that accounts for the activation of the different coverages and predicts the individual payments that they might incur. Using the framework of multinomial logistic regressions, we model the activation of the different insurance coverages for each claim and their subsequent development in the following years, i.e. the activation of other coverages in the later years and all the possible payments that might result from them. As such, we obtain predictions for the future payments at the level of the different coverages activated by each claim rather than at the claim-level only. We use a recent insurance automobile dataset from a major Canadian insurance company with claims information provided for four different insurance coverages from 2015 to mid-2021.

In this article, we apply non-convex regularization methods in order to obtain stable estimation of loss development factors in insurance claims reserving. Among the non-convex regularization methods, we focus on the use of the log-adjusted absolute deviation (LAAD) penalty and provide discussion on optimization of LAAD penalized regression model, which we prove to converge with a coordinate descent algorithm under mild conditions. This has the advantage of obtaining a consistent estimator for the regression coefficients while allowing for the variable selection, which is linked to the stable estimation of loss development factors. We calibrate our proposed model using a multi-line insurance dataset from a property and casualty insurer where we observed reported aggregate loss along accident years and development periods. When compared to other regression models, our LAAD penalized regression model provides very promising results.

A central part of an insurance company is the management of its future cash flows and solvency capital. To this end, insurers have to set aside reserves to cover outstanding claims liabilities. Macro-level reserving models such as the chain-ladder, focus on aggregated data organized in a so- called run-off triangle and produce reserves for the whole portfolio. Micro-level reserving models use claim-specific data to produce reserves for individual claims. Machine learning models have been proposed for the task of micro-level reserving. These machine learning models can detect non- linear associations and process large amount of structured or unstructured data, hence are expected to perform better than classical macro-level reserving models. However, such machine learning micro-level models have not been compared to each other leading to a fragmented literature. In this presentation, we propose a comparative study of such machine learning models and investigate their properties on both simulated and real individual claims data from an insurance company. Different lines of business as well as different performance measures are used to highlight the characteristics and trade-offs in the different model architectures. Joint work with R.V. Oirbeek and T. Verdonck.

I provide an overview on the estimation of enterprise capital via Monte Carlo methods. I discuss nested simulations, approaches based on least-squares regression (regress now or later), and approaches based on Machine Learning. I focus on comparing different methods based theoretical and numerical analysis.

A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

With nonnegative support and discrete mass at zero, the Tweedie model becomes a popular method to analyze the continuous zero-spike insurance claim data. However, the traditional Tweedie model will not take the spatial pattern into account while the spatial correlation is fairly common in this type of data. Motivated by this issue, we propose a Tweedie model with the conditional autoregressive prior. The Bayesian approach to our proposed model is discussed to avoid the sophisticated mathematical calculations caused by the complication of Tweedie’s density function. Also, we conduct a sensitivity analysis for selecting the optimal priors for our model. In addition, we implement a simulation study to assess our model’s performance and further apply it to the insurance data on the auto claims payments in U.S. dollars for 100,169 clients in the state of Idaho, USA.

As catastrophic events happen more and more frequently, accurately forecasting risk at a higher level is vital for the financial stability of the insurance industry. This paper proposes an efficient three-step procedure to predict extreme risk in insurance ratemaking . The first step uses logistic regression for estimating the nonzero claim probability. The second step employs quantile regression for selecting a dynamic threshold. The third step fits a generalized Pareto distribution to exceedances over the chosen threshold. A random weighted bootstrap method is employed to quantify the uncertainty of the final risk forecast. We also apply the method to an automobile insurance dataset.

In property insurance claims triage, insurers often use static information to assess the severity of a claim and identify the subsequent actions. We hypothesize that the pattern of weather conditions throughout the course of the loss event is predictive of insured losses and hence appropriate use of weather dynamics improve the operation of insurer's claim management. To test this hypothesis, we propose a deep learning method to incorporate the dynamic weather data in the predictive modeling of insured losses for reported claims. The proposed method features a hierarchical network architecture to address the challenges introduced into claims triage by weather dynamics. In the empirical analysis, we examine a portfolio of hail damage property insurance claims obtained from a major U.S. insurance carrier. When supplemented by the dynamic weather information, the deep learning method exhibits substantial improvement in the hold-out predictive performance. Built upon the proposed deep learning method, we design a cost-sensitive decision strategy for triaging claims using the probabilistic forecasts of insurance claim amounts. We show that leveraging weather dynamics in claims triage lead to a substantial reduction in operational cost.

Recent transformative and disruptive developments in the insurance industry embrace various InsurTech innovations. Particularly with the rapid advances in data science and computational infrastructure, InsurTech is able to incorporate multiple emerging sources of data and reveal implications for value creation on business insurance by enhancing current insurance operations. In this paper, we unprecedently combine real-life proprietary insurance claims information and features, empowered by InsurTech, describing insured businesses to create enhanced tree-based loss models. Empirical study shows that the supplemental data sources created by InsurTech innovation help significantly improve the underlying insurance company's in-house or internal pricing models. We further demonstrate how InsurTech proliferates firm-level value creation and affect insurance product development, pricing, underwriting, claim management and administration practice.

While random effects models have been widely used to analyze the general insurance datasets, likelihood functions of such models are usually complicated so that naïve applications of general optimization methods may direct us to local maxima. In this article, we propose a novel algorithm to calibrate compound risk models with longitudinal data. More specifically, we provide a detailed example of our algorithm to Poisson/gamma frequency model and gamma/inverse-gamma model, respectively. It is shown the proposed EM algorithm provides us more accurate and stable results compared to general optimization methods.

With the emergence of machine learning within insurance, actuaries have many flexible tools at their disposal to improve the predictive performance of their pricing models. A major inconvenience with the main algorithms for machine learning regression (gradient boosting machines and neural networks) is ignoring the uncertainty associated with the model parameters. Additionally, few machine learning models predict correlated response variables. To circumvent these weaknesses, we present deep Bayesian neural networks for insurance pricing, a flexible machine learning framework that captures process and parameter uncertainties. By studying neural networks within the Bayesian framework, we can capture both sources of uncertainties, providing a better tool to diagnose when the model predictions are confident or not. We introduce the model, propose methods to estimate the parameters and present inference strategies. We also explain how one may use deep Bayesian neural networks to predict dependent outcomes with FGM copulas. Finally, we explain how one may use deep Bayesian neural networks to model dependent outcomes with an FGM copula.

Technological advances in weather data collection allow insurers to incorporate high-resolution data to manage hail risk more effectively, but challenges arise when the response variable and predictors are collected from different locations. To address this issue, we adopt a spatial point pattern viewpoint for modeling hail insurance claims. In particular, we propose a spatial mixed-effects framework for replicated point patterns to model the frequency and geographical distribution of hail dam- age claims following a hailstorm. Our model simultaneously incorporates traditional property rating characteristics collected from policyholders, as well as densely collected weather features, even when observed at different sets of locations across a region. We discuss likelihood-based inference and demonstrate parameter estimation with simulation studies. Using hail damage insurance claims data from a U.S. insurer, supplemented with hail radar maps and other spatially varying weather features, we show that incorporating granular data to model the development of claim reporting patterns helps insurers anticipate and manage claims more efficiently. Joint work with P. Shi.

In this talk, the insurance portfolio risk retention problem will be explored in a context where the underlying risk may experience dependence at the granular level. Given a set of retention parameters for a risk, including a deductible, an upper limit, and a coinsurance, both the policyholder and the insurance company may be interested in finding out the influence of a small change in each risk retention parameter. Furthermore, it may be useful for both the policyholder and the insurance company to determine the parameter that results in the smallest amount of increase in risk when changed, given a specific target insurance premium for the company’s retained portion of the risk. In order to compare the influence of the marginal changes in the risk retention parameters, the RM2 risk measure can be used. In the talk, I will explain how the RM2 risk measure can be used in this context, using simple real world examples, and explain how the risk retention problem can be influenced by dependence at the granular level of the risk. The computation of the RM2 may be challenging for a general aggregate claims model based on dependent claim frequencies and severities, and I will share some of the advancements made in this area as well.

In actuarial practice, maximum likelihood estimation (MLE) is an exclusively adopted approach to estimate parameters of claim distributions. Despite of its popularity, MLE often suffers from robustness issues where the estimated model can be heavily distorted by small model contaminations. Two common robustness issues include: (i) Tail robustness: perturbations on small claims may severely distort the estimated tail distributions, providing misleading risk management information; (ii) Outlier robustness: estimated parameters are heavily influenced by few outliers, resulting to unreliable fitted model. To alleviate the above robustness problem, we propose a maximum weighted likelihood estimator (MWLE) which reduces the weights of the observations which are likely to cause unrobustness. Asymptotic theories are developed to ensure that MWLE is consistent and asymptotically normal, so that model uncertainties can be easily quantified. The proposed MWLE is also highly versatile, as it can be easily extended to cater for several mechanisms prevalent in insurance practice, including the impacts of policyholder attributes (regression) and loss control mechanisms (e.g. data censoring and/or truncation). As a side-product, one may also create a Wald-based test statistic based on the MWLE. This diagnostic tool quantitatively detects systematic incoherence of fitted model class, providing recommendations whether it is worthwhile to explore alternative model classes.

In this talk, we will discuss algorithmic biases, actuarial fairness and possible discrimination, in the context where actuaries can use more and more data, as well as more complex (black box) models. We will present several examples, and try to discuss mathematical definition of "fairness".

This article explores a way to approximate credibility premium for claims frequency when there is an indication of zero-inflation or multiple claim coverages are considered. The proposed method enables insurance companies to capture unobserved heterogeneity of policyholders in various ratemaking models with modest computation costs and interpretable credibility formulas. According to simulation studies, the proposed method outperforms pre-existing benchmarks in terms of prediction performances and computation time. Finally, the applicability of proposed method is assessed with a real data analysis with multiple coverages and it is shown that such approximation of multivariate credibility premium could be more useful when past claims experience for a line of business is not enough but the experience from the other lines can be borrowed.

One of the silver linings of the COVID pandemic is that it has forced actuarial academics to move beyond traditional face-to-face teaching methods, sometimes known as the "sage on the stage," and consider supplement teaching with computer-driven tools. In this talk, I describe a completed open source project developed by 15 collaborators from 4 countries. The purpose of our pilot project, under the auspices of ASTIN, the non-life section of the International Actuarial Association, is to provide a series of tutorials on Loss Data Analytics. The site is https://openacttextdev.github.io/LDACourse1/. This is one of several projects being sponsored by the ASTIN Academy, the working group of the ASTIN section that is sponsoring actuarial open educational resources. We hope that workshop participants will learn from this resource, encourage students and colleagues to also do so, and consider contributing to our efforts as we seek to provide open educational resources to the actuarial profession.

This presentation will look at Covid-19 mortality experience (mainly in the 50+ age group) and what impact this has had over the last two years and might have on future mortality. We will first look at how Covid-19 mortality experience compares with all-cause mortality using English data, once we have allowed for varying infection rates across the population. A key conclusion is that there is a strong proportionality relationship between Covid-19 death rates and all-cause mortality by age and by socio-economic group (e.g. by deprivation). What we then observe as higher death rates in specific groups can then mainly be attributable to variations in infection rates (e.g. regional or socio-economic variation). Second, we will look at the future mortality prospects for those who survive the pandemic. A simple model will be presented that allows us to explore this question. In the absence of secondary effects of the pandemic, survivors are likely to be healthier than the pre-pandemic population, with a corresponding small increase in life expectancies. However, further adjustments will need to be made when we begin to quantify the secondary impacts of Covid including long-term impairments ("long Covid") and the impact of delayed treatments for other illnesses such as cancers.

I will discuss several interrelated projects on analyzing longevity jointly across several populations. The approach is to employ Multi-Output Gaussian Processes (MOGP), a spatial machine learning method, to smooth and extrapolate multiple Age-Period mortality surfaces across populations that may be indexed by Countries, Genders, Cause-of-Death, etc. To maintain flexibility and scalability, we investigate MOGPs with Kronecker-structured kernels and latent factors for dimension reduction and computational speed up. In particular, we develop a custom multi-level MOGP that leverages the gridded structure of mortality tables to efficiently capture heterogeneity and dependence across different factor inputs. Results are illustrated with datasets from the Human Mortality Database (HMD) and include case studies across EU nations and genders, as well as analysis of cause-of-death datasets for European countries and in the US. Our models provide insights into the commonality of mortality trends and demonstrate the opportunities for respective data fusion. This is joint work with Nhan Huynh.

The lifestyles and backgrounds of individuals across the United States differ widely. Some of these differences are easily measurable (ethnicity, age, income, etc.) while others are not (stress levels, empathy, diet, exercise, etc.). Though every person is unique, individuals living closer together likely have more similar lifestyles than individuals living hundreds of miles apart. Because lifestyle and environmental factors contribute to mortality, spatial correlation may be an important feature in mortality modeling. However, many of the current mortality models fail to account for spatial relationships. This paper introduces spatio-temporal trends into traditional mortality modeling using Bayesian hierarchical models with conditional auto-regressive (CAR) priors. We show that these priors, commonly used for areal data, are appropriate for modeling county-level spatial trends in mortality data covering the contiguous United States. We find that mortality rates of neighboring counties are highly correlated. Additionally, we find that mortality improvement or deterioration trends between neighboring counties are also highly correlated. Joint work with Zoe Gibbs, Robert RIchardson, and Chris Groendyke.

Data breach incidents result in severe financial loss and reputational damage, which raises the importance of using insurance to manage and mitigate cyber-related risks. We analyze data breach chronology collected by Privacy Rights Clearinghouse (PRC) since 2005 and propose a generalized linear mixed model . Our model captures not only frequency and severity information of cyber losses, but also time effect trends due to dependency between frequency and severity. Types of breach and organization and spatial location characteristics in chronology are taken as covariates to investigate their effects on breach frequencies. The yearly frequency is estimated under Bayesian framework using a combination of Gibbs sampler and Metropolis-Hastings algorithm. Predictions and applications of the proposed model in cyber insurance are discussed.

In the past decade, cyber insurance has raised much interest in the insurance indus- try, and cyber risk has evolved from a type of pure operational risk to both operational and liability risk for insurers. However, the modeling of cyber risk is still in its infancy. Compared with typical insurance risks, cyber risk has some unique features. In particular, discrete variables regularly arise both in the frequency component (e.g. number of events per unit time), and the severity component (e.g. the number of data breaches for each cyber event). In addition, the modeling of these count variables are further complicated by nonstandard properties such as zero inflation, serial and cross-sectional correlations, as well as heavy tails. Previous cyber risk models have largely focused on continuous models that are incompatible with many of these characteristics. This paper introduces a new count-based frequency-severity framework to the insurance literature, with a dynamic multivariate negative binomial autoregressive process for the frequency component, and the generalized Poisson inverse-Gaussian distribution for the severity component. We unify these new modeling tools by proposing a tractable Generalized Method of Moments for their estimation and apply them to the Privacy Rights Clearinghouse (PRC) dataset. Joint work with W. Zhu and J. Zhang.

We study the problem of active portfolio management where an investor aims to outperform a benchmark strategy's risk profile while not deviating too far from it. Specifically, an investor considers alternative strategies whose terminal wealth lie within a Wasserstein ball surrounding a benchmark's - being distributionally close - and that have a specified dependence/copula - tying state-by-state outcomes - to it. The investor then chooses the alternative strategy that minimises a distortion risk measure of terminal wealth. In a general (complete) market model, we prove that an optimal dynamic strategy exists and provide its characterisation through the notion of isotonic projections. We further propose a simulation approach to calculate the optimal strategy's terminal wealth, making our approach applicable to a wide range of market models. Finally, we illustrate how investors with different copula and risk preferences invest and improve upon the benchmark using the Tail Value-at-Risk, inverse S-shaped, and lower- and upper-tail distortion risk measures as examples. We find that investors' optimal terminal wealth distribution has larger probability masses in regions that reduce their risk measure relative to the benchmark while preserving the benchmark's structure.

In this talk, I’ll construct a general risk model R(t) based on Hawkes process [1] (we call it General compound Hawkes process (GCHP) [4,5,6]), and then I’ll discuss two applications of this risk model in insurance: 1) Merton investment problem [2,3,6] and 2) optimal investment with liability [5,7]. For the first problem 1), an investor starts with initial capital, R(o)=u, and then wishes to decide how much money to invest into risky and risk-free assets to maximize the capital. For the second problem 2), we consider a continuous-time mean–variance portfolio selection model with multiple risky assets and one liability in an incomplete market with the goal to maximize the expected terminal wealth while minimizing the variance of the terminal wealth [5,7]. The risky assets’ prices are governed by geometric Brownian motions while the liability described by the GCHP [4,6]. We solve both problems by using diffusion approximation for the GCHP. In problem 1) we construct and solve HJB equation for the expected utility function [6]. The second problem 2) is solved by applying general stochastic linear-quadratic control technique [5,7]. References: 1. Hawkes, A.G., 1971. Spectra of some self-exciting and mutually exciting point processes. Biometrika 58 (1), 83–90. http://dx.doi.org/10.1093/biomet/58.1. 83. 2. Merton, R. (1969). Lifetime portfolio selection under uncertainty: The continuous-time case. The Review of Econ. Stat., 247-257. 3. Merton, R. (1971). Optimum consumption and portfolio rules in a continuous-time model. J. of Economic Theory. 3, 373-413. 4. Swishchuk, A. (2018): Risk model based on general compound Hawkes process. Wilmott, v. 2018, Issue 94. 5. Swishchuk, A., Zagst, R. and Zeller, G. (2020): Hawkes processes in insurance: Risk model, application to empirical data and optimal investment. Insurance: Mathematics and Economics, https://doi.org/10.1016/j.insmatheco.2020.12.005. 6. Swishchuk, A. (2021): Merton Investment problems in finance and insurance for the Hawkes-based models. Risks 2021, 9, 108. https://doi.org/10.3390/risks9060108 7. Xie, S., Li, Z. and Wang, S. (2008): Continuous-time portfolio selection with liability: mean-variance model and stochastic LQ approach. Insurance: Mathematics and Economics, 42(3),943-953, http://dx.doi.org/10.1016/j.insmatheco.2007.10.014.

In this presentation, we propose a complex economic scenario generator that nests versions of well-known actuarial frameworks. The generator estimation relies on the Bayesian paradigm and accounts for both model and parameter uncertainty via Markov chain Monte Carlo methods. So, to the question is less more?, we answer maybe, but it depends on your criteria. From an in-sample fit perspective, on the one hand, a complex economic scenario generator seems better. From the conservatism, forecasting, and coverage perspectives, on the other hand, the situation is less clear: having more complex models for the short rate, term structure, and stock index returns is clearly beneficial. However, that is not the case for inflation and the dividend yield. Towards the end of the presentation, we also provide a brief discussion on next possible extensions of this research. Among others, the idea of creating ensemble models to cope with model risk will be discussed.

One way to quantify uncertainty in risk evaluations in a financial or actuarial setting is using sensitivity analysis, where one studies the relationship between the variability in model outputs and uncertainty in model inputs. We build on a particular type of sensitivity analysis called reverse sensitivity testing, which has recently been introduced in the literature. We generalise the reverse sensitivity framework by developing a methodology applicable to Levy-Ito processes, which proceeds as follows: First, we introduce a stress to a stochastic process by increasing a risk measure evaluated at the process’s terminal time. Second, we derive the stressed probability measure under which the stochastic process fulfils the stress and that has minimal Kullback-Leibler divergence. We study the characteristics of the stochastic process under the stressed probability measure and illustrate them using numerical experiments.

While deep learning models lead to very competitive regression models, often outperforming classical statistical models such as generalized linear models, the disadvantage is that deep learning solutions are difficult to interpret and explain, and variable selection is not easily possible. In this talk we consider two new directions in designing explainable deep learning models. The first of these is the Combined Actuarial Explainable Neural Network (CAXNN), which builds on a popular neural network architecture in the actuarial literature. We demonstrate the CAXNN model on a mortality modeling problem. Secondly, inspired by the appealing structure of generalized linear models, we present a new network architecture, the LocalGLMnet, that shares similar features as generalized linear models, but provides superior predictive power benefiting from the art of representation learning. This new architecture allows for variable selection of tabular data and for interpretation of the calibrated deep learning model.

5-day workshop participants are welcome to use BIRS facilities (TCPL ) until 3 pm on Friday, although participants are still required to checkout of the guest rooms by 11AM.