Time-dependent Risk Model Research Articles

Uniform asymptotic estimates in a time-dependent risk model with general investment returns and multivariate regularly varying claims

Consider an insurer with d lines of business and the freedom to make risk-free and risky investments. The investment portfolio price process is described as a general càdlàg process. It is assumed that the claim sizes from different lines of business and their common inter-arrival times form a sequence of independent and identically distributed (i.i.d.) random pairs, each pair obeying a particular dependence structure. With this dependence structure, claim sizes from different lines of business are distributed according to the multivariate regular variation. This paper proposes conditions that can be satisfied by several important stochastic processes, including the Lévy process, Vasicek interest rate model, Cox-Ingersoll-Ross interest rate model, Heston model, and Stochastic volatility model. Under these conditions, the uniform asymptotic expansions of ruin probabilities are derived, which hold uniformly for the entire time horizon. Numerical examples are provided as a means of illustrating the main results.

Estimates for the Finite-Time Ruin Probability of a Time-Dependent Risk Model with a Brownian Perturbation

In this paper, we consider a time-dependent risk model with a Brownian perturbation. In this model, there is a dependence structure between the claim sizes and their corresponding interarrival times. Assuming the claim sizes have subexponential distributions, we obtain the asymptotic lower bound of the finite-time ruin probability. When the claim sizes have distributions from the class L∩D, the asymptotic upper bound of the finite-time ruin probability has been presented. These results confirm that when the claim sizes are heavy-tailed, the asymptotics of the finite-time ruin probability of this time-dependent model are insensitive to the Brownian perturbation.

The finite-time ruin probability of time-dependent risk model with stochastic return and Brownian perturbation

This paper considers a dependent risk model with stochastic return and Brownian perturbation, where there exists a dependence structure between the claim sizes and the inter-arrival times and the price process of the investment portfolio is a geometric Levy process. When the claim sizes have heavy-tailed distributions, the asymptotic lower and upper bounds of the finite-time ruin probability have been given.

Large deviations for the discounted aggregate claims in time-dependent risk model with constant interest force

This paper achieves the weakly asymptotic formulas of the large deviations for the discounted aggregate claims in a time-dependent risk model with widely upper orthant dependent and dominatedly-varying- tailed claims, where the time-dependence structure is defined by a conditional tail probability of the claim size given the inter-arrival time before the claim. Further, if the claims are consistently varying tailed or regularly varying tailed, some asymptotic formulas of the large deviations are established.

Asymptotic results for ruin probability in a two-dimensional risk model with stochastic investment returns

This paper considers a two-dimensional time-dependent risk model with stochastic investment returns. In the model, an insurer operates two lines of insurance businesses sharing a common claim number process and can invest its surplus into some risky assets. The claim number process is assumed to be a renewal counting process and the investment return is modeled by a geometric Lévy process. Furthermore, claim sizes of the two insurance businesses and their common inter-arrival times correspondingly follow a three-dimensional Sarmanov distribution. When claim sizes of the two lines of insurance businesses are heavy tailed, we establish some uniform asymptotic formulas for the ruin probability of the model over certain time horizon. Also, we show the accuracy of these asymptotic estimates for the ruin probability under the risk model by numerical studies.

Tail behavior for the sum of two correlated classes of discounted aggregate claims in a time-dependent risk model

ABSTRACTConsider a continuous-time risk model with two correlated classes of insurance business and a constant force of interest. Suppose that the correlation comes from a common shock, and that the claim sizes and inter-arrival times correspondingly form a sequence of random pairs, with each pair obeying a dependence structure. By assuming that the claim sizes are heavy tailed, a uniform tail asymptotic formula for the sum of the two correlated classes of discounted aggregate claims is obtained.

Uniform asymptotics for a multi-dimensional time-dependent risk model with multivariate regularly varying claims and stochastic return

This paper is devoted to asymptotic analysis for a multi-dimensional risk model with a general dependence structure and stochastic return driven by a geometric Lévy process. We take into account both the dependence among the claim sizes from different lines of businesses and that between the claim sizes and their common claim-number process. Under certain mild technical conditions, we obtain for two types of ruin probabilities precise asymptotic expansions which hold uniformly for the whole time horizon.

Uniformly asymptotic behavior for the tail probability of discounted aggregate claims in the time-dependent risk model with upper tail asymptotically independent claims

ABSTRACTIn this paper, we consider the tail behavior of discounted aggregate claims in a dependent risk model with constant interest force, in which the claim sizes are of upper tail asymptotic independence structure, and the claim size and its corresponding inter-claim time satisfy a certain dependence structure described by a conditional tail probability of the claim size given the inter-claim time before the claim occurs. For the case that the claim size distribution belongs to the intersection of long-tailed distribution class and dominant variation class, we obtain an asymptotic formula, which holds uniformly for all times in a finite interval. Moreover, we prove that if the claim size distribution belongs to the consistent variation class, the formula holds uniformly for all times in an infinite interval.

Uniformly asymptotic behavior of ruin probabilities in a time-dependent renewal risk model with stochastic return

In this paper, we consider a time-dependent risk model, where an insurance company is allowed to invest its wealth in financial assets and the price process of the investment portfolio is described as a geometric Lévy process. When claim sizes have dominatedly varying tails, we obtain some asymptotic formulae for ruin probabilities holding uniformly for some finite or infinite time horizons. We further perform some simulations to check the accuracy of our formulae.

Uniform Asymptotics for the Finite-Time Ruin Probability of a Time-Dependent Risk Model with Pairwise Quasiasymptotically Independent Claims

We consider a generalized time-dependent risk model with constant interest force, where the claim sizes are of pairwise quasiasymptotical independence structure, and the claim size and its interclaim time satisfy a dependence structure defined by a conditional tail probability of the claim size given the interclaim time before the claim occurs. As the claim-size distribution belongs to the dominated variation class, we establish some weakly asymptotic formulae for the tail probability of discounted aggregate claims and the finite-time ruin probability, which hold uniformly for all times in a relevant infinite interval.

Extremes on the discounted aggregate claims in a time dependent risk model

This paper presents an extension of the classical compound Poisson risk model for which the inter-claim time and the forthcoming claim amount are no longer independent random variables (rv's). Asymptotic tail probabilities for the discounted aggregate claims are presented when the force of interest is constant and the claim amounts are heavy tail distributed rv's. Furthermore, we derive asymptotic finite time ruin probabilities, as well as asymptotic approximations for some common risk measures associated with the discounted aggregate claims. A simulation study is performed in order to validate the results obtained in the free interest risk model.

Development and validation of a time-dependent risk model for predicting mortality in infective endocarditis

Existing risk models in infective endocarditis (IE) have not investigated whether the prognostic value of clinical parameters is time-dependent. We have explored the potential of time-dependent risk stratification to predict outcome in IE. We studied 273 patients admitted with IE to two centres (derivation cohort n=192, validation cohort n=81). The derivation cohort was used to identify independent predictors of 6 months mortality at days 1, 8, and 15 (multivariable Cox regression, P<0.05). There were six predictors at day 1, five at day 8, and only three at day 15. Whereas heart failure, thrombocytopenia, and severe comorbidity predicted mortality at all three time-points, other predictors were time-dependent (age, tachycardia, renal impairment at day 1; severe embolic events, renal impairment at day 8). These predictors were incorporated into a time-dependent model. The model was validated in an independent cohort with concordance indices of 0.79 (95% CI 0.68-0.91) at day 1, 0.79 (95% CI 0.65-0.93) at day 8, and 0.84 (95% CI 0.73-0.95) at day 15. Six months mortality was 2.4% in patients deemed as low-risk at all time-points, compared with 78.2% in patients classified as high-risk at any evaluation. Prognostic factors in IE are time-dependent. Time-dependent risk stratification accurately predicts outcome in IE.

On Some Limit Theorems Similar to the Arc-Sin Law

On Some Limit Theorems Similar to the Arc-Sin Law