Economics - Research Publications
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ItemAn n-year roll forward reserve model for social long term care insurance in Australia( 2005-02)We propose an n-year roll forward reserve model for a social LTC insurance scheme that may be introduced in Australia. Using the projected future needs and costs of LTC as derived in Leung (2004a), we calculate the likely contribution requirements to maintain 1-year, 2-year and 4-year level roll forward reserves for a hypothetical Australian Commonwealth government administered social LTC insurance scheme in Australia and to derive short term reserve profiles for such a fund over the next 50 years.
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ItemSecond order Bayesian revision of a generalised linear model( 2005-05)It is well known that the exponential dispersion family (EDF) of univariate distributions is closed under Bayesian revision in the presence of natural conjugate priors. However, this is not the case for the general multivariate EDF. This paper derives a second order approximation to the posterior likelihood of a naturally conjugated generalised linear model (GLM), i.e. multivariate EDF subject to alink function (Section 5.5). It is not the same as a normal approximation. It does, however, lead to second order Bayes estimators of parameters of the posterior.The family of second order approximations is found to be closed under Bayesian revision. This generates a recursion for repeated Bayesian revision of the GLM with theacquisition of additional data. The recursion simplifies greatly for a canonical link. The resulting structure is easily extended to a filter for estimation of the parameters of a dynamic generalised linear model (DGLM) (Section 6.2). The Kalman filter emerges as a special case.A second type of link function, related to the canonical link, and with similar properties, is identified. This is called here the companion canonical link. For a given GLM with canonical link, the companion to that link generates a companion GLM (Section 4). The recursive form of the Bayesian revision of this GLM is also obtained (Section5.5.3). There is a perfect parallel between the development of the GLM recursion and its companion. A dictionary for translation between the two is given so that one is readilyderived from the other (Table 5.1). The companion canonical link also generates a companion DGLM. A filter for this isobtained (Section 6.3).
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ItemThe Distribution of the Dividend Payments in theCompound Poisson Risk Model Perturbed byDiffusion( 2005-02)We consider a diffusion perturbed classical compound Poisson risk model in the presence of a constant dividend barrier. An integro-differential equation with certain boundary conditions for the n-th moment of the discounted dividend payments prior to ruin is derived and solved. Its solution can be expressed in terms of the expected discounted penalty (Gerber-Shiu) functions due to oscillation in the corresponding perturbed risk model without a barrier. When the discount factor is zero, we show that all the results can be expressed in terms of the non-ruin probability in the perturbed risk model without a barrier.
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ItemFitting combinations of exponentials to probability distributions( 2005-11)Two techniques are described for approximating distributions on the positive half-line by combinations of exponentials. One is based on Jacobi polynomial expansions, and the other on the log-beta distribution. The techniques are applied to some well-known distributions (degenerate, uniform, Pareto, lognormal and others). In theory the techniques yield sequences of combination of exponentials that always converge to the true distribution, but their numerical performance depends on the particular distribution being approximated. An error bound is given in the case the log-beta approximations.
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ItemExploring unknown quantities : development and application of a stochastic catastrophe model with output and sensitivities( 2005-05)Stochastic catastrophe models are now widely used to assess and manage catastrophe exposure. In Australia, natural perils are the focus of modelling, havinghistorically caused substantial insured losses. The proprietary nature of commonly used models has resulted in limited public scrutiny of their workings – despite the existence of significant inconsistencies in cross-model output. This paper adds to the currently limited body of publicly available literature regarding the detail of catastrophe model development. This is done through a thorough presentation of a theoretical model and the application of this model to the peril of hailstorm in the Sydney region for commercial property insurance. It is found that data is difficult to obtain, placing constraints on the model design. Additionally, the sensitivity of output to changes in assumptions and parameters is highly significant – supporting the argument for greater cross-model comparison. Finally, it is suggested that increased co-operation and openness would help to address the causes of model inconsistency and improve the overall standard of catastrophe modelling
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ItemSynchronous bootstrapping of seemingly unrelated regressions( 2005-08)Consider the seemingly unrelated regression framework, in which regression models are applied to a number of data sets, with stochastic dependencies between them. The regression models are not restricted to general linear models (e.g. GLMs). Forecasts are required, with estimates of prediction errors that account for the dependencies between data sets. Bootstrapping is used to estimate prediction errors. Specialised forms of bootstrapping that capture the dependencies are constructed.Insurance and banking applications are mentioned. The former is investigated with numerical examples. The specific context is insurance loss reserving under the requirement that the entire distribution of loss reserve be estimated, where this reserve is aggregated across a number of stochastically dependent lines of business.
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ItemOptimal Dividends under a Ruin ProbabilityConstraint( 2005-10)We consider a classical surplus process modified by the paymentof dividends when the insurer’s surplus exceeds a threshold. We use aprobabilistic argument to obtain general expressions for the expected present value of dividend payments, and show how these expressions can be applied for certain individual claim amount distributions. We then consider the question of maximising the expected present valueof dividend payments subject to a constraint on the insurer’s ruin probability.
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ItemFourier inversion formulas in option pricingand insurance( 2005-12)Several authors have used Fourier inversion to compute optionprices. In insurance, the expected value of max(S − K, 0) also arisesin excess-of-loss or stop-loss insurance, and similar techniques maybe used. Lewis (2001) used Parseval’s theorem to find formulas foroption prices in terms of the characteristic function of the log-price.This paper aims at taking the same idea further: (1) formulas requiringweaker assumptions; (2) relationship with classical inversiontheorems; (3) formulas for payoffs which occur in insurance.
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ItemRent seeking and judicial bias in weak legal systems( 2005-01)We model rent seeking in litigation in weak legal systems as a Tullochcontest in which litigators may seek to influence the court directly throughbribery as well as through the merit of the legal case that they bring. Ifthe local firm has a competitive advantage in influencing the court thenthere is a strategic asymmetry between the players: the local firm regardsexpenditure by the foreign firm as a strategic complement, but the for-eign firm regards local expenditure as a strategic substitute. This leads todifferent attitudes to commitment: the local firm would like to commit toa high level of effort to influence the court, the foreign firm to a low one.There is also an asymmetry in the commitment technology. It is not easyto commit to a low level of bribery, but it is feasible to commit to a highone: once a payment is made it cannot easily be recovered. We modelthe interaction as a two stage game: the players simultaneously committo a minimum level of effort, then they play a simultaneous Tulloch influ-ence game. We find a continuum of equilibria. An equilibrium selectionargument selects a unique equilibrium that is outcome equivalent to theStackelberg equilibrium of a simple Tulloch contest in which the local firmmoves first. We thus find an argument for endogenous timing: the localfirm moves first and secures a first mover advantage.
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ItemEstimating and Combining National IncomeDistributions using Limited Data( 2005-02)A major problem encountered in studies of income inequality at regional and globallevels is the estimation of income distributions from data that are in a summary form.In this paper we estimate national and regional income distributions within a generalframework that relaxes the assumption of constant income within groups. A techniqueto estimate the parameters of a beta-2 distribution using grouped data is proposed.Regional income distribution is modelled using a mixture of country-specificdistributions and its properties are examined. The techniques are used to analysenational and regional inequality trends for eight East Asian countries and twobenchmark years, 1988 and 1993.