Economics - Research Publications
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ItemOn the optimality of joint periodic and extraordinary dividend strategies(ELSEVIER, 2021-08-13)In this paper, we model the cash surplus (or equity) of a risky business with a Brownian motion (with a drift). Owners can take cash out of the surplus in the form of “dividends”, subject to transaction costs. However, if the surplus hits 0 then ruin occurs and the business cannot operate any more. We consider two types of dividend distributions: (i) periodic, regular ones (that is, dividends can be paid only at countably many points in time, according to a specific arrival process); and (ii) extraordinary dividend payments that can be made immediately at any time (that is, the dividend decision time space is continuous and matches that of the surplus process). Both types of dividends attract proportional transaction costs, but extraordinary distributions also attract fixed transaction costs, which is a realistic feature. A dividend strategy that involves both types of distributions (periodic and extraordinary) is qualified as “hybrid”. We determine which strategies (either periodic, immediate, or hybrid) are optimal, that is, we show which are the strategies that maximise the expected present value of dividends paid until ruin, net of transaction costs. Sometimes, a liquidation strategy (which pays out all monies and stops the process) is optimal. Which strategy is optimal depends on the profitability of the business, and the level of (proportional and fixed) transaction costs. Results are illustrated.
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ItemSynthETIC: An individual insurance claim simulator with feature control(ELSEVIER, 2021-07-07)Recent years have seen rapid increase in the application of machine learning to insurance loss reserving. They yield most value when applied to large data sets, such as individual claims, or large claim triangles. In short, they are likely to be useful in the analysis of any data set whose volume is sufficient to obscure a naked-eye view of its features. Unfortunately, such large data sets are in short supply in the actuarial literature. Accordingly, one needs to turn to synthetic data. Although the ultimate objective of these methods is application to real data, the use of synthetic data containing features commonly observed in real data is also to be encouraged. While there are a number of claims simulators in existence, each valuable within its own context, the inclusion of a number of desirable (but complicated) data features requires further development. Accordingly, in this paper we review those desirable features, and propose a new simulator of individual claim experience called SynthETIC. Our simulator is publicly available, open source, and fills a gap in the non-life actuarial toolkit. The simulator specifically allows for desirable (but optionally complicated) data features typically occurring in practice, such as variations in rates of settlements and development patterns; as with superimposed inflation, and various discontinuities, and also enables various dependencies between variables. The user has full control of the mechanics of the evolution of an individual claim. As a result, the complexity of the data set generated (meaning the level of difficulty of analysis) may be dialed anywhere from extremely simple to extremely complex. The default version is parameterized so as to include a broad (though not numerically precise) resemblance to the major features of experience of a specific (but anonymous) Auto Bodily Injury portfolio, but the general structure is suitable for most lines of business, with some amendment of modules.
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ItemOn the modelling of multivariate counts with Cox processes and dependent shot noise intensities(ELSEVIER, 2021-04-03)In this paper, we develop a method to model and estimate several, dependent count processes, using granular data. Specifically, we develop a multivariate Cox process with shot noise intensities to jointly model the arrival process of counts (e.g. insurance claims). The dependency structure is introduced via multivariate shot noise intensity processes which are connected with the help of Lévy copulas. In aggregate, our approach allows for (i) over-dispersion and auto-correlation within each line of business; (ii) realistic features involving time-varying, known covariates; and (iii) parsimonious dependence between processes without requiring simultaneous primary (e.g. accidents) events.
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ItemOptimal periodic dividend strategies for spectrally negative Levy processes with fixed transaction costs(Taylor and Francis Group, 2021-02-04)Maximising dividends is one classical stability criterion in actuarial risk theory. Motivated by the fact that dividends are paid periodically in real life, periodic dividend strategies were recently introduced (Albrecher et al. 2011). In this paper, we incorporate fixed transaction costs into the model and study the optimal periodic dividend strategy with fixed transaction costs for spectrally negative Lévy processes. The value function of a periodic (bu,bl) strategy is calculated by means of exiting identities and Itô's excusion when the surplus process is of unbounded variation. We show that a sufficient condition for optimality is that the Lévy measure admits a density which is completely monotonic. Under such assumptions, a periodic (bu,bl) strategy is confirmed to be optimal. Results are illustrated.
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ItemNo Preview AvailableA counterexample to the existence of a general central limit theorem for pairwise independent identically distributed random variables(ACADEMIC PRESS INC ELSEVIER SCIENCE, 2021-07-01)
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ItemNo Preview AvailableOn unbalanced data and common shock models in stochastic loss reserving(Cambridge University Press (CUP), 2021-03-01)Introducing common shocks is a popular dependence modelling approach, with some recent applications in loss reserving. The main advantage of this approach is the ability to capture structural dependence coming from known relationships. In addition, it helps with the parsimonious construction of correlation matrices of large dimensions. However, complications arise in the presence of "unbalanced data", that is, when (expected) magnitude of observations over a single triangle, or between triangles, can vary substantially. Specifically, if a single common shock is applied to all of these cells, it can contribute insignificantly to the larger values and/or swamp the smaller ones, unless careful adjustments are made. This problem is further complicated in applications involving negative claim amounts. In this paper, we address this problem in the loss reserving context using a common shock Tweedie approach for unbalanced data. We show that the solution not only provides a much better balance of the common shock proportions relative to the unbalanced data, but it is also parsimonious. Finally, the common shock Tweedie model also provides distributional tractability.
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ItemNo Preview AvailableModelling and understanding count processes through a Markov-modulated non-homogeneous Poisson process framework(Elsevier BV, 2021-04-01)The Markov-modulated Poisson process is utilised for count modelling in a variety of areas such as queueing, reliability, network and insurance claims analysis. In this paper, we extend the Markov-modulated Poisson process framework through the introduction of a flexible frequency perturbation measure. This contribution enables known information of observed event arrivals to be naturally incorporated in a tractable manner, while the hidden Markov chain captures the effect of unobservable drivers of the data. In addition to increases in accuracy and interpretability, this method supplements analysis of the latent factors. Further, this procedure naturally incorporates data features such as over-dispersion and autocorrelation. Additional insights can be generated to assist analysis, including a procedure for iterative model improvement. Implementation difficulties are also addressed with a focus on dealing with large data sets, where latent models are especially advantageous due the large number of observations facilitating identification of hidden factors. Namely, computational issues such as numerical underflow and high processing cost arise in this context and in this paper, we produce procedures to overcome these problems. This modelling framework is demonstrated using a large insurance data set to illustrate theoretical, practical and computational contributions and an empirical comparison to other count models highlight the advantages of the proposed approach.
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ItemOptimal periodic dividend strategies for spectrally positive Lévy risk processes with fixed transaction costs(Elsevier BV, 2020-07-01)We consider the general class of spectrally positive Lévy risk processes, which are appropriate for businesses with continuous expenses and lump sum gains whose timing and sizes are stochastic. Motivated by the fact that dividends cannot be paid at any time in real life, we study periodic dividend strategies whereby dividend decisions are made according to a separate arrival process. In this paper, we investigate the impact of fixed transaction costs on the optimal periodic dividend strategy, and show that a periodic strategy is optimal when decision times arrive according to an independent Poisson process. Such a strategy leads to lump sum dividends that bring the surplus back to as long as it is no less than at a dividend decision time. The expected present value of dividends (net of transaction costs) is provided explicitly with the help of scale functions. Results are illustrated.
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ItemA multivariate evolutionary generalised linear model framework with adaptive estimation for claims reserving(Elsevier, 2020-07-01)In this paper, we develop a multivariate evolutionary generalised linear model (GLM) framework for claims reserving, which allows for dynamic features of claims activity in conjunction with dependency across business lines to accurately assess claims reserves. We extend the traditional GLM reserving framework on two fronts: GLM fixed factors are allowed to evolve in a recursive manner, and dependence is incorporated in the specification of these factors using a common shock approach. We consider factors that evolve across accident years in conjunction with factors that evolve across cal-endar years. This two-dimensional evolution of factors is unconventional as a traditional evolutionary model typically considers the evolution in one single time dimension. This creates challenges for the estimation process, which we tackle in this paper. We develop the formulation of a particle filtering algorithm with parameter learning procedure. This is an adaptive estimation approach which updates evolving factors of the framework recursively over time. We implement and illustrate our model with a simulated data set, as well as a set of real data from a Canadian insurer.