Economics - Research Publications
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ItemDividend and Capital Injection Optimization with Transaction Cost for Levy Risk Processes(SPRINGER/PLENUM PUBLISHERS, 2022-09)Abstract The optimal dividends problem has remained an active research field for decades. For an insurance company with reserve modelled by a spectrally negative Lévy process having finite first-order moment, we study the optimalimpulse dividend and capital injection(IDCI) strategy for maximizing the expected accumulated discounted net dividend payment subtracted by the accumulated discounted cost of injecting capital. In this setting, the beneficiary of the dividends injects capital to ensure a non-negative risk process so that the insurer never goes bankrupt. The optimal IDCI strategy together with its value function is obtained. Besides, two numerical examples are provided to illustrate the features of the optimal strategies. The impacts of model parameters are also studied.
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ItemDiscrete-Time Risk Models with Claim Correlated Premiums in a Markovian Environment(MDPI, 2021-01-01)In this paper we consider a discrete-time risk model, which allows the premium to be adjusted according to claims experience. This model is inspired by the well-known bonusmalus system in the non-life insurance industry. Two strategies of adjusting periodic premiums are considered: aggregate claims or claim frequency. Recursive formulae are derived to compute the finite-time ruin probabilities, and Lundberg-type upper bounds are also derived to evaluate the ultimate-time ruin probabilities. In addition, we extend the risk model by considering an external Markovian environment in which the claims distributions are governed by an external Markov process so that the periodic premium adjustments vary when the external environment state changes. We then study the joint distribution of premium level and environment state at ruin given ruin occurs. Two numerical examples are provided at the end of this paper to illustrate the impact of the initial external environment state, the initial premium level and the initial surplus on the ruin probability.
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ItemOn the Type I multivariate zero-truncated hurdle model with applications in health insurance(Elsevier, 2020-01-01)In the general insurance modeling literature, there has been a lot of work based on univariate zero-truncated models, but little has been done in the multivariate zero-truncation cases, for instance a line of insurance business with various classes of policies. There are three types of zero-truncation in the multivariate setting: only records with all zeros are missing, zero counts for one or some classes are missing, or zeros are completely missing for all classes. In this paper, we focus on the first case, the so-called Type I zero-truncation, and a new multivariate zero-truncated hurdle model is developed to study it. The key idea of developing such a model is to identify a stochastic representation for the underlying random variables, which enables us to use the EM algorithm to simplify the estimation procedure. This model is used to analyze a health insurance claims dataset that contains claim counts from different categories of claims without common zero observations.
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ItemOptimal implementation delay of taxation with trade-off for spectrally negative Lévy risk processes(Springer Verlag, 2021)In this paper we consider two cases of optimal implementation delay of taxation with trade-off under spectrally negative Lévy insurance risk processes. In the first case, we assume that the insurance company starts to pay tax only when its surplus level reaches a certain level, and at the termination time of the business there is a terminal value incurred to the company. A method is developed to determine the optimal starting-tax surplus level at which the total expected discounted value of all tax payments up to the termination time plus the discounted terminal value is maximized. In the second case, the company still pays tax subject to a starting-tax surplus level, but with capital injections to prevent bankruptcy. The total expected discounted value of tax payments minus the total discounted capital injection costs is maximized to determine the optimal starting-tax surplus level. Numerical examples are given at the end to illustrate the existence of positive optimal starting-tax surplus levels for both cases considered in this paper.
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ItemA Projection of Future Hospitalisation Needs in a Rapidly Ageing Society: A Hong Kong Experience(MDPI AG, 2019-02-01)To assess the impact of ageing on hospitalisation in a rapidly ageing society. A study using retrospective and prospective data was conducted using hospitalisation data with age-specific admission rates in the period from 2001–2010 and demographic data from the period of 2001–2066 by the United Nations. The Hong Kong Special Administrative Region (SAR) with a 7 million population experiences extreme low fertility (1.1 children per woman) and long life expectancy (84 years old). Days of hospitalisation: For the period 2010–2066, the length of stay (LOS) in the age group 85+ is projected to increase by 555.3% while the LOS for the whole population is expected to increase by only 134.4% and by ageing only. In 2010, the proportion in the LOS contributed to by the oldest age group (85+) was 15%. In 2066, this proportion is projected to nearly triple (42%). Around 70% of the projected days of hospitalisation would be taken by people aged 75 years and above. It is projected that this phenomenon would be converted to a more balanced structure when the demographic transition changes into a more stable distribution. Apparently, the impact of ageing on the public hospital system has not been well understood and prepared. The determined result provides insight into monitoring the capacity of the hospital system to cope with a rapidly changing demographic society. It provides empirical evidence of the impact of ageing on the public hospitalisation system. It gives a long term projection up to the year 2066 while the situation would be different from the transient period of 2016–2030. The analysis adopts a fixed rate approach, which assumes the LOS to be only driven by demographic factors, while any improvements in health technologies and health awareness are not accounted for. Only inpatient data from the Hospital Authority were used, nonetheless, they are the best available for the study. Due to the limitation of data, proximity to death is not controlled in conducting this analysis.
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ItemOn a discrete-time risk model with claim correlated premiums(Cambridge University Press, 2015-09)This paper proposes a discrete-time risk model that has a certain type of correlation between premiums and claim amounts. It is motivated by the well-known bonus-malus system (also known as the no claims discount) in the car insurance industry. Such a system penalises policyholders at fault in accidents by surcharges, and rewards claim-free years by discounts. For simplicity, only up to three levels of premium are considered in this paper and recursive formulae are derived to calculate the ultimate ruin probabilities. Explicit expressions of ruin probabilities are obtained in a simplified case. The impact of the proposed correlation between premiums and claims on ruin probabilities is examined through numerical examples. In the end, the joint probability of ruin and deficit at ruin is also considered.
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ItemOn the prediction of claim duration for income protection insurance policyholders(Cambridge University Press, 2014-03)This paper explores how we can apply various modern data mining techniques to better understand Australian Income Protection Insurance (IPI). We provide a fast and objective method of scoring claims into different portfolios using available rating factors. Results from fitting several prediction models are compared based on not only the conventional loss prediction error function, but also a modified loss function. We demonstrate that the prediction power of all the data mining methods under consideration is clearly evident using a misclassification plot. We also point out that this predictability can be masked by looking at just the conventional prediction error function. We then suggest using the stepwise regression technique to reduce the number of variables used in the data mining methods. Apart from this variable selection method, we also look at principal components analysis to increase understanding of the rating factors that drive claim durations of insured lives. We also discuss and compare how different variable combining techniques can be used to weight available predicting variables. One interesting outcome we discover is that principal components analysis and the weighted combination prediction model together provide very consistent results on identifying the most significant variables for explaining claim durations.
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ItemSurvival Analysis of Left Truncated Income Protection Insurance Data(Walter de Gruyter GmbH, 2013)One of the main characteristics of Income Protection Insurance (IPI) claim duration data, which has not been considered in the actuarial literature on the topic, is left-truncation. Claimants that are observed are those whose sickness durations are longer than the deferred periods specified in the policies, and hence left-truncation exists in these data. This paper investigates a series of conditional mixture models when applying survival analysis to model sickness durations of IPI claimants, and examines the consequence of treating the IPI data with lengthy deferred periods as complete data and therefore ignoring the left-truncation by fitting the corresponding unconditional distributions. It also quantifies the extent of the bias in the resulting parameter estimates when ignoring the left-truncation in the data. Using the UK Continuous Mortality Investigation (CMI) sickness duration data, some well-fitting survival model results are estimated. It is demonstrated that ignoring the left-truncation in certain IPI data can lead to substantially different statistical estimates. We therefore suggest taking left-truncation into account by fitting conditional mixture distributions to IPI data. Furthermore, the best fitting model is extended by introducing a number of covariates into the conditional part to do regression analysis.
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ItemA Bayesian Approach to Parameter Estimation for Kernel Density Estimation via Transformations(Cambridge University Press, 2011)In this paper, we present a Markov chain Monte Carlo (MCMC) simulation algorithm for estimating parameters in the kernel density estimation of bivariate insurance claim data via transformations. Our data set consists of two types of auto insurance claim costs and exhibits a high-level of skewness in the marginal empirical distributions. Therefore, the kernel density estimator based on original data does not perform well. However, the density of the original data can be estimated through estimating the density of the transformed data using kernels. It is well known that the performance of a kernel density estimator is mainly determined by the bandwidth, and only in a minor way by the kernel. In the current literature, there have been some developments in the area of estimating densities based on transformed data, where bandwidth selection usually depends on pre-determined transformation parameters. Moreover, in the bivariate situation, the transformation parameters were estimated for each dimension individually. We use a Bayesian sampling algorithm and present a Metropolis-Hastings sampling procedure to sample the bandwidth and transformation parameters from their posterior density. Our contribution is to estimate the bandwidths and transformation parameters simultaneously within a Metropolis-Hastings sampling procedure. Moreover, we demonstrate that the correlation between the two dimensions is better captured through the bivariate density estimator based on transformed data.
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ItemEquilibrium distributions of discrete phase type(Marcel Dekker Inc., 2013)It is well known that the family of discrete phase-type distributions is closed under convolutions, mixtures, and the unary “geometric mixture” operation. In this article, we show that the equilibrium distributions of this family are again of phase type. A simple result is obtained for the limiting equilibrium distributions; that is, the equilibrium distributions of any discrete phase-type distribution with an irreducible representation always converge to a geometric distribution. Numerical examples are provided in three different cases. At the end of the article, a more general type of equilibrium distribution is considered to which a discount factor is introduced.