Dependent Risk Model Research Articles

Dependent Insurance Risk Model: Deterministic Threshold

This article considers a dependent insurance risk model. We assume that the inter-arrival time depends on the previous claim size through a deterministic threshold structure. Adjustment coefficient and Lundberg-type upper bound for the ruin probability are obtained. In case of exponential claim size, an explicit solution for the ruin probability is obtained by solving a system of ordinary delay differential equations. Some numerical results are included for illustration purposes.

Asymptotics for ruin probability of some negatively dependent risk models with a constant interest rate and dominatedly-varying-tailed claims

This paper deals with some negatively dependent risk models with a constant interest rate, dominatedly-varying-tailed claims and a general premium process. We first establish two weak asymptotic equivalent formulae for the finite-time ruin probabilities. Furthermore, we obtain a uniform result for the dependent renewal risk model with a constant premium rate.

A perturbed risk model with dependence between premium rates and claim sizes

This paper considers a dependent risk model with diffusion for the surplus of an insurer, in which a current premium rate will be adjusted after a claim occurs and the adjusted rate is determined by the amount of the claim. At the same time, the diffusion is changed correspondingly. Using Rouché’s theorem, we first derive the closed-form solution for the Laplace transform of the survival probability in the dependent risk model. Then, using the Laplace transform, we derive a defective renewal equation satisfied by the survival probability. For the exponential claim sizes, we present the explicit recursion expression for the survival probability, by which we can exactly solve the survival probability step-by-step. We also illustrate the influence of the model parameters in the dependent risk model on the survival probability by numerical examples.

Asymptotics for tail probability of total claim amount with negatively dependent claim sizes and its applications

In this paper, we obtain the asymptotics for the tail probability of the total claim amount with negatively dependent claim sizes in two cases: in the first case, the distribution tail of the claim number is dominatedly varying; in the second case, the distribution of the claim number is in the maximum domain of attraction of the Gumbel distribution, and the claim sizes are light-tailed. In both cases, we assume that the claim sizes are nondegenerate negatively dependent and identically distributed random variables and that the claim number is not necessarily independent of the claim sizes. As applications, we derive asymptotics for the finite-time ruin probabilities in some dependent compound renewal risk models with constant interest rate.

Upper bounds for ruin probabilities in two dependent risk models under rates of interest

In this article, we consider two discrete-time risk models, in which dependent structures of the payments and the interest force are considered. Two autoregressive moving-average (ARMA) models are introduced to model the premiums and rates of interest, and the claims are assumed to be independent. Generalized Lundberg inequalities for the ruin probabilities are derived by using renewal recursive technique, which extend some known results. Copyright © 2009 John Wiley & Sons, Ltd.

Asset proportions in optimal portfolios with dependent default risks

In this note, we consider the dependent default risk model of factor type. The dependence between the returns of assets is driven by default indicators. Sufficient conditions on the dependence structure of default indicators and on the utility function are investigated which enable one to order the optimal amount invested in each asset. We thus complement one result in [Cheung, K.C., Yang, H., 2004. Ordering optimal proportions in the asset allocation problem with dependent default risks. Insurance: Math. Econom. 35, 595–609].

On two dependent individual risk models

In this paper, we propose two constructions which allow dependence between the risks of an insurance portfolio in the individual risk model. In the first construction, each risk’s experience is influenced by an individual and a collective risk factor, as well as a class factor if the portfolio is divided into different classes. The second construction uses copulas. The impact on the cumulative distribution function of the aggregate claim amount and on the stop-loss premium is presented via numerical examples.

Stochastic Dependence in Competing Risks

spells may terminate via multiple outcomes: the term of a cabinet, for example, may end with or without an election; wars persist until the loss or victory of the aggressor. Analysts typically assume stochastic independence among risks, the duration modeling equivalent of independence of irrelevant alternatives. However, many political examples violate this assumption. I review competing risks as a latent variables approach. After discussing methods for modeling dependence that place restrictions on the nature of association, I introduce a parametric generalized dependent risks model in which inter-risk correla?

Risk models for flood levee design

In the design of flood levee systems there are many parameters and variables with associated uncertainties. This paper presents models which systematically analyze the various types of uncertainties in the hydrologic aspect as well as hydraulic aspect of design and analysis to define the risk and reliability of overtopping. Both static and time dependent risk models are developed. Results show that risk evaluated by the simple return period method can be underestimated by 10% to 50%, depending on the loading distribution model used. The risk‐safety factor relationships are shown to be very sensitive to the hydrologic loading probability model adopted, so that composite models are suggested for risk analysis.

On Some Limit Theorems Similar to the Arc-Sin Law

On Some Limit Theorems Similar to the Arc-Sin Law