Browse Research
Viewing 101 to 125 of 188 results
2014
Actuaries quite often have to interpolate data to obtain quantities such as loss development factors (LDFs) for maturities in between the maturities included in a loss development triangle, or increased limits factors for limits between the data points used in the increased limits analysis.
2014
In the present paper we consider the claims reserving problem in a multivariate context. More precisely, we apply the multivariate generalization of the well-known credibility model proposed by Bühlmann and Straub (1970) to claims reserving.
2014
Copula models have been popular in risk management. Due to the properties of asymptotic dependence and easy simulation, the t-copula has often been employed in practice. A computationally simple estimation procedure for the t-copula is to first estimate the linear correlation via Kendall’s tau estimator and then to estimate the parameter of the number of degrees of freedom by maximizing the pseudo likelihood function.
2014
Retention is an important factor that impacts both profit and growth of insurance companies. Conventional retention analysis, such as logistic regression, does not distinguish between two types of attrition: mid-term cancellation and end-term nonrenewal. In this paper, the authors propose to use survival analysis to estimate attrition and retention.
2014
When estimating loss reserves, actuaries usually give varying weights to multiple indications to arrive at their final selected indication. The common practice is to give weight to indications that have been developed to their ultimate expected amount.
2014
A firm will replace a physical asset at the end of its useful life. This fact demonstrates that there is a notion of mortality implicit in the way an enterprise manages its physical assets. We propose a theory that there is also an efficient time to replace a physical asset that is random and observable.
2014
This paper back-tests the popular over-dispersed Poisson bootstrap of the paid chain-ladder model from England and Verrall(2002), using data from hundreds of U.S. companies, spanning three decades. The results show that the modeled distributions underestimate reserve risk. We investigate why this may occur, and propose two methods to increase the variability of the distribution to pass the back-test.
2013
Maximum likelihood estimators provide a powerful statistical tool. In this paper we directly deal with non-linear reserving models, without the need to transform those models to make them tractable for linear or generalized linear methods.
2013
Property-casualty insurance companies tend to buy reinsurance; when they do, they must address reinsurance credit risk.
2013
This paper tackles the question: why should split credibility be better than credibility without a split? It corrects previous misunderstandings and presents new formulas showing how parameter uncertainty is reduced by use of unsplit credibility and then how it might be further reduced by introduction of a split. It derives the formulas for unsplit and split credibility when losses follow the widely used collective risk model (CRM).
2013
In many applied claims reserving problems in P&C insurance, the claims settlement process goes beyond the latest development period available in the observed claims development triangle. This makes it necessary to estimate so-called tail development factors which account for the unobserved part of the insurance claims. We estimate these tail development factors in a mathematically consistent way.
2013
This paper studies an insurance model under the regulation that the insurance company has to reserve sufficient initial capital to ensure that ruin probability does not exceed the given quantity a. We prove the existence of the minimum initial capital. To illustrate our results, we give an example in approximating the minimum initial capital for exponential claims.
2013
The current industry standard approach evaluates reinsurance effectiveness by calculating capital cost savings as the product of a fixed capital cost rate and the required capital which is released. Reinsurance is deemed value-creating if the resulting capital cost savings is more than the profit margin ceded to support the purchase-a Return On Risk-Adjusted Capital (RORAC) approach.
2013
In their short paper, the authors describe an elegant decision rule for evaluating the attractiveness of potential reinsurance transactions. In effect, they propose comparing the premium quoted by reinsurers for a particular reinsurance structure to the portion of its premiums the ceding company would need to allocate, given its cost of capital, to retain the risk.
2013
This paper presents a Bayesian technique for adjusting a mixed exponential severity distribution in response to partially-credible observed claim severities. It presents two applications: pricing excess of loss (XOL) reinsurance layers and computing increased limits factors (ILFs). The paper’s Bayesian model uses a Dirichlet distribution over the mixed exponential’s initial mixture weights.
2013
This paper adopts the extreme value and VaR approach to investigate the amount of rice damaged due to extreme events and analyzes the collective risk model as a feasible scheme for estimating annual aggregate losses. The results show that the annual frequency of rice damage caused by typhoons is shown to fit well the Poisson distribution with one parameter.
2013
Two recent papers by Dornheim and Brazauskas (2011a, 2011b) introduced a new likelihood-based approach for robust-efficient fitting of mixed linear models and showed that it possesses favorable large and small-sample properties which yield more accurate premiums when extreme outcomes are present in the data.
2012
There is a dearth of public knowledge about the development patterns of mature workers compensation claims at the level of the aggregate loss triangle; this is because there are only a few loss triangles available for research that span the full lifetime of the cohort of claimants.
2012
Predictive models are used by insurers for underwriting and ratemaking in personal lines insurance. Focusing on homeowners insurance, this paper examines many predictive generalized linear models, including those for pure premium (Tweedie), frequency (logistic) and severity (gamma). We compare predictions from models based on a single peril, or cause of loss, to those based on multiple perils.
2012
After laying a fairly rigorous foundation for the mathematical treatment of excess losses, this paper shows that the excess-loss function is akin to the probability distribution of its loss. All the moments of the loss can be reclaimed from the excess-loss function, the variance being especially simple. Excess-loss mathematics is a powerful tool for pricing loss layers, as in reinsurance.
2012
This paper presents a methodology for constructing a deterministic approximation to the distribution of the outputs produced by the loss development method (also known as the chain-ladder method). The approximation distribution produced by this methodology is designed to meet a preset error tolerance condition.
2012
It is generally well established that new business produces higher loss and expense ratios and lower retention ratios than renewal business. Ironically, to add more new business, an insurer needs higher profitability in order to generate the additional capital needed to support its exposure growth. Irrational growth is one of the op reasons for the insolvencies of property and casualty insurance companies.
2012
The aim of this paper is to analyze the impact of underwriting cycles on the risk and return of non-life insurance companies. We integrate underwriting cycles in a dynamic financial analysis framework using a stochastic process, specifically, the Ornstein-Uhlenbeck process, which is fitted to empirical data and used to analyze the impact of these cycles on risk and return.
2012
The models of Mack (1993) and Murphy (1994) are expanded to a continuously indexed family of chain-ladder models by broadening the variance structure of the error term. It is shown that, subject to certain restrictions, an actuary’s selected report-to-report factor can be considered the best linear unbiased estimate for some member of this family.
2012
Existing models of the market price of cat bonds are often too exotic or too simplistic; we present a model that is grounded in theory yet also tractable. We also intend for our analysis of cat bond pricing to shed light on broader issues relating to the theory of risk pricing.
