Browse Research
Viewing 1301 to 1325 of 7690 results
2010
We first present a simple matrix-based recursive formula for calculating the distribution function of compound phase-type random variables. Then we extend the results to the case when the number of claims follows a bivariate matrix negative binomial (BMNB) distribution detailed herein.
2010
In this paper, we discuss how to define conservative biometric bases in life insurance. The first approach is based on cumulative hazard (or survival probabilities), the second one on the hazard itself, and the third one on the rate of increase of the hazard. The second case has been studied in the literature and the sum-at-risk plays a central role in defining safe-side requirements.
2010
This paper aims at providing a mathematical foundation for the terms of the well spread supervisory rule “initial market value of assets must be at least equal to provision plus solvency capital”.
It starts with a risk-adjusted assessment — given by a set of test probabilities — of the future cash-flows coming from a company business plan and attempts to define terms of a supervisory accounting mode.
2010
When analyzing catastrophic risk, traditional measures for evaluating risk, such as the probable maximum loss (PML), value at risk (VaR), tail-VaR, and others, can become practically impossible to obtain analytically in certain types of insurance, such as earthquake, and certain types of reinsurance arrangements, specially non-proportional with reinstatements.
2010
This study incorporates the survival analysis of unemployment duration into the insurance pricing framework to measure the fairly priced premium rate for Taiwan’s unemployment insurance (UI) program.
2010
In this paper we consider a reinsurance syndicate, assuming that Pareto optimal allocations exist. Under a continuity assumption on preferences, we show that a competitive equilibrium exists and is unique. Our conditions allow for risks that are not bounded, and we show that the most standard models satisfy our set of sufficient conditions, which are thus not restrictive.
2010
We tackle problems that appear in the practical application of the Mack method for the estimation of reserving risk and the bootstrapping of ultimate reserve distributions. More specifically, we design a filter for outliers and large jumps, and present a robust version of Mack’s variance estimator. A combination of these guarantees a reasonable Mack and bootstrap error even for deficient data.
2010
Under new solvency regulations, general insurance companies need to calculate a risk margin to cover possible shortfalls in their liability runoff. A popular approach for the calculation of the risk margin is the so-called cost-of-capital approach. A comprehensive cost-of-capital approach involves the consideration of multiperiod risk measures.
2010
The probability of ruin in continuous and finite time is numerically evaluated in a classical risk process where the premium can be updated according to credibility models and therefore change from year to year. A major consideration in the development of this approach is that it should be easily applicable to large portfolios. Our method uses as a first tool the model developed by Afonso et al.
2010
We consider estimating tail events using exponential families of importance sampling distributions. When the cannonical sufficient statistic for the exponential family mimics the tail behaviour of the underlying cumulative distribution function, we can achieve bounded relative error for estimating tail probabilities. Examples of rare event simulation from various distributions including Tukey’s g&h distribution are provided.
2010
A general ‘multivariate’ decomposition of covariances is formulated and proved, and its role in the context of financial risk measurement and pricing is demonstrated.
Keywords: Covariance decompositions; insurance pricing; economic pricing; weighted allocations; capital asset pricing model.
2010
In this paper, we aim to evaluate the distribution of the aggregate claims in the collective risk model. The claim count distribution is firstly assumed to belong to a generalised (a, b, 0) family. A matrix form recursive formula is then derived to evaluate the related compound distribution when individual claim amounts follow a discrete distribution on non-negative integers.
2010
This paper aims to provide accurate approximations for the quantiles of the conditional expected present value of the payments made by the annuity provider, given the future path of the Lee-Carter time index. Conditional cohort and period life expectancies are also considered.
2010
A methodology for pricing of reinsurance contracts in the presence of a catastrophe bond is developed. An important advantage of this approach is that it allows for the pricing of reinsurance contracts consistent with the observed market prices of catastrophe bonds on the same underlying risk process.
2010
In this paper, we consider the dual of the classical Cramér-Lundberg model when gains follow a phase-type distribution. By using the property of phase-type distribution, two pairs of upcrossing and downcrossing barrier probabilities are derived.
2010
A critical problem in financial and insurance risk analysis is the calculation of risk margins. When there are a number of risks, the total risk margin is often reduced to reflect diversification. How large should the "diversification benefit" be? And how should the benefit be allocated to to the individual risks? We propose a simple statistical solution.
2010
In this paper, we reexamine the two optimal reinsurance problems studied in Cai et al. (2008), in which the objectives are to find the optimal reinsurance contracts that minimize the value-at-risk (VaR) and the conditional tail expectation (CTE) of the total risk exposure under the expectation premium principle. We provide a simpler and more transparent approach to solve these problems by using intuitive geometric arguments.
2010
Some extensions to the delayed renewal risk models are considered. In particular, the independence assumption between the interclaim time and the subsequent claim size is relaxed, and the classical Gerber-Shiu penalty function is generalized by incorporating more variables. As a result, general structures regarding various joint densities of ruin related quantities as well as their probabalistic interpretations are provided.
2010
The priamary objective of the paper is to explore using reinsurance as a risk management tool for an insurance company. We consider an insurance company whose surplus can be modeled by a Brownian motion with drift and that the surplus can be invested in a risky or riskless asset.
2010
In this paper we consider various specifications of the general discrete-time risk model in which a serial dependence structure is introduced between the claim numbers for each period.
2010
This paper deals with the numberical computation of the optimal form of reinsurance from the ceding company point of view, when the cedent seeks to maximize the adjustment coefficient of the retained risk and the reinsurance loading is an increasing function of the variance.
We compare the optimal treaty with the best stop loss policy.
2010
In recent years, market consistent-valuation approaches have gained an increasing importance for the insurance companies. This has triggered an increasing interest among practitioners and academics, and a number of specific studies on such valuation approaches have been published.
In this paper, we present a generic model for the valuation of life insurance contracts and embedded options.
2010
Regulation of insurers' use of genetic information means actuaries are interested in age-at-onset of genetic disorders. Arjas & Haara (1984)suggested Market Point Processes (MPPs) as useful models for life history data with complex covariates.
2010
In the aftermath of the 2007-2008 financial crisis, there has been a criticism of mathematics and the mathematical models used by the finance industry. We answer these criticisms through a discussion of some of the actuarial models used in the pricing of credit derivatives. As an example, we focus in particular on the Gaussian copula model and its drawbacks.
2010
It is common for professional associations and regulators to combine the claims of several insurers into a database known as an "intercompany" experience data set. In this paper, we analyze data on claims accounts provided by the General Insurance Association of Singapore, an organization consisting of most of the general insurers in Singapore.
