Uniform asymptotics for finite-time ruin probability in some dependent compound risk models with constant interest rate

Consider two dependent renewal risk models with constant interest rate. By using some methods in the risk theory, uniform asymptotics for finite-time ruin probability is derived in a non-compound risk model, where claim sizes are upper tail asymptotically independent random variables with dominatedly varying tails, claim inter-arrival times follow the widely lower orthant dependent structure, and the total amount of premiums is a nonnegative stochastic process. Based on the obtained result, using the method of analysis for the tail probability of random sums, a similar result in a more complex and reasonable compound risk model is also obtained, where individual claim sizes are specialized to be extended negatively dependent and accident inter-arrival times are still widely lower orthant dependent, and both the claim sizes and the claim number have dominatedly varying tails.

RUIN PROBABILITY IN THE CONTINUOUS-TIME COMPOUND BINOMIAL MODEL WITH INVESTMENT

This article deals with the problem of minimizing ruin probability under optimal control for the continuous-time compound binomial model with investment. The jump mechanism in our article is different from that of Liu et al [4]. Comparing with [4], the introduction of the investment, and hence, the additional Brownian motion term, makes the problem technically challenging. To overcome this technical difficulty, the theory of change of measure is used and an exponential martingale is obtained by virtue of the extended generator. The ruin probability is minimized through maximizing adjustment coefficient in the sense of Lundberg bounds. At the same time, the optimal investment strategy is obtained.

Estimates for the ruin probability of a time-dependent renewal risk model with dependent by-claims

Consider a continuous-time renewal risk model, in which every main claim induces a delayed by-claim. Assume that the main claim sizes and the inter-arrival times form a sequence of identically distributed random pairs, with each pair obeying a dependence structure, and so do the by-claim sizes and the delay times. Supposing that the main claim sizes with by-claim sizes form a sequence of dependent random variables with dominatedly varying tails, asymptotic estimates for the ruin probability of the surplus process are investigated, by establishing a weakly asymptotic formula, as the initial surplus tends to infinity.

Ruin Probability with Variable Premium Rate and Disturbed by Diffusion in a Markovian Environment

We consider a risk model with a premium rate which varies with the level of free reserves. In this model, the occurrence of claims is described by a Cox process with Markov intensity process, and the influence of stochastic factors is considered by adding a diffusion process. The integro-differential equation for the ruin probability is derived by a infinitesimal method. Key words ruin probability - variable premium rate - diffusion process - Markov intensity CLC number O 211.9 Foundation item: Supported by the National Natural Science Foundation of China (10071058, 70273029)

Survival probability and ruin probability of a risk model

In this paper, a new risk model is studied in which the rate of premium income is regarded as a random variable, the arrival of insurance policies is a Poisson process and the process of claim occurring is p-thinning process. The integral representations of the survival probability are gotten. The explicit formula of the survival probability on the infinite interval is obtained in the special casc cxponential distribution.The Lundberg inequality and the common formula of the ruin probability are gotten in terms of some techniques from martingale theory.

Ruin probability for correlated negative risk sums model with Erlang processes

This paper studies a Sparre Andersen negative risk sums model in which the distribution of ＂interclaim＂ time is that of a sum of n independent exponential random variables. Thus, the Erlang（n） model is a special case. On this basis the correlated negative risk sums process with the common Erlang process is considered. Integro-differential equations with boundary conditions for ψ（u） are given. For some special cases a closed-form expression for ψ（u） is derived.

A Local Asymptotic Behavior for Ruin Probability in the Renewal Risk Model

Let R（t）=u＋ct-∑ I=1^N（t） Xi,t≥0 be the renewal risk model, with Fx（x）being the distribution function of the claim amount X. Let ψ（u） be the ruin probability with initial surplus u. Under the condition of Fx（x） ∈ S^＊（γ）,y ≥ 0, by the geometric sum method, we derive the local asymptotic behavior for ψ（u,u ＋ z] for every 0 （ z （ oo, On one hand, the asymptotic behavior of ψ（u） can be derived from the result obtained. On the other hand, the result of this paper can be applied to the insurance risk management of an insurance company.

The finite-time ruin probability in the presence of Sarmanov dependent financial and insurance risks

Consider a discrete-time insurance risk model. Within period i, i≥ 1, Xi and Yi denote the net insurance loss and the stochastic discount factor of an insurer, respectively. Assume that {（Xi, Yi）, i≥1） form a sequence of independent and identically distributed random vectors following a common bivariate Sarmanov distribution. In the presence of heavy-tailed net insurance losses, an asymptotic formula is derived for the finite-time ruin probability.

Ruin Probability of One Kind of Entrance Processes Based Insurance Risk Models

In this note,one kind of insurance risk models with the policies having multiple validity times are investigated.Explicit expressions for the ruin probabilities are obtained by using the martingale method.As a consequence,the obtained probability serves as an upper bound for the ruin probability of a newly developed entrance processes based risk model.

Finite Time Ruin Probability with Variable Interest Rate and Extended Regular Variation

Consider an insurance risk model, in which the surplus process satisfies a recursive equationU n =U n?1(1+r n )?X n forn≥1, whereU 0=x≥0 is the initial surplus, {r n ;n≥1} the interest rate sequence, {X n ;n≥1} the sequence of i. i. d. real-valued random variables with common distribution functionF, which denotes the gross loss during thenth year. We investigate the ruin probability within a finite time horizon and give the asymptotic result asx→∞. Key words variable interest rate - extend regular variation - finite time ruin probability CLC number O 211.9 Foundation item: Supported by the National Natural Science Foundation of China (10071058, 70273029)Biography: WEI Xiao (1979-), female, Ph. D candidate, research direction: large deviations and its applications, insurance mathematics.

Research on Ruin Probability of Risk Model Based on AR(1)Time Series

The insurance industry typically exploits ruin theory on collected data to gain more profits.However,state-of-art approaches fail to consider the dependency of the intensity of claim numbers,resulting in the loss of accuracy.In this work,we establish a new risk model based on traditional AR(1)time series,and propose a fine-gained insurance model which has a dependent data structure.We leverage Newton iteration method to figure out the adjustment coefficient and evaluate the exponential upper bound of the ruin probability.We claim that our model significantly improves the precision of insurance model and explores an interesting direction for future research.

A Decomposition of the Ruin Probability for Risk Process with Vasicek Interest Rate

In this paper, it is assumed that an insurer with a jump-diffusion risk process would invest its surplus in a bond market, and the interest structure of the bond market is assumed to follow the Vasicek interest model. This paper focuses on the studying of the ruin problems in the above compounded process. In this compounded risk model, ruin may be caused by a claim or oscillation. We decompose the ruin probability for the compounded risk process into two probabilities： the probability that ruin caused by a claim and the probability that ruin caused by oscillation. Integro-differential equations for these ruin probabilities are derived. When the claim sizes are exponentially distributed, the above-mentioned integro-differential equations can be reduced into a three-order partial differential equation.

Optimal New Business for Insurer to Minimize the Ruin Probability under Interest Force

Under constant interest force, the risk processes for old and new insurance business are modelled by Brownian motion with drift. By the stochastic control method, the explicit expressions for the minimum ruin probability and the corresponding optimal strategy are derived. Numerical example shows that the minimum probability of ruin and the optimal proportion for new business decrease as the interest rate increases, and vice versa.

Locally and globally uniform approximations for ruin probabilities of a nonstandard bidimensional risk model with subexponential claims

Consider a nonstandard continuous-time bidimensional risk model with constant force of interest,in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair of the claim-inter-arrival times is arbitrarily dependent.Under some mild conditions,we achieve a locally uniform approximation of the finite-time ruin probability for all time horizon within a finite interval.If we further assume that each pair of the claim-inter-arrival times is negative quadrant dependent and the two classes of claims are consistently-varying-tailed,it shows that the above obtained approximation is also globally uniform for all time horizon within an infinite interval.

Ruin Probability in Linear Time Series Model

This paper analyzes a continuous time risk model with a linear model used to model the claim process. The time is discretized stochastically using the times when claims occur, using Doob’s stopping time theorem and martingale inequalities to obtain expressions for the ruin probability as well as both expo- nential and non-exponential upper bounds for the ruin probability for an infinite time horizon. Numerical re- sults are included to illustrate the accuracy of the non-exponential bound.

FINITE-TIME RUIN PROBABILITY WITH NQD DOMINATED VARYING-TAILED CLAIMS AND NLOD INTER-ARRIVAL TIMES

In 2007,Chen and Ng investigated infinite-time ruin probability with constant interest forceand negatively quadrant dependent and extended regularly varying-tailed claims.Following this work,the authors obtain a weakly asymptotic equivalent formula for the finite-time and infinite-time ruinprobability with constant interest force,negatively quadrant dependent,and dominated varying-tailedclaims and negatively lower orthant dependent inter-arrival times.In particular,when the claims areconsistently varying-tailed,an asymptotic equivalent formula is presented.

Estimates for the Finite-time Ruin Probability with Insurance and Financial Risks

The paper gives estimates for the finite-time ruin probability with insurance and financial risks. When the distribution of the insurance risk belongs to the class L（γ） for some γ〉0 or the subexponential distribution class, we abtain some asymptotic equivalent relationships for the finite-time ruin probability, respectively. When the distribution of the insurance risk belongs to the dominated varying-tailed distribution class, we obtain asymptotic upper bound and lower bound for the finite-time ruin probability, where for the asymptotic upper bound, we completely get rid of the restriction of mutual independence on insurance risks, and for the lower bound, we only need the insurance risks to have a weak positive association structure. The obtained results extend and improve some existing results.

The Finite-time Ruin Probability for the Jump-Diffusion Model with Constant Interest Force

In this paper, we consider the finite time ruin probability for the jump-diffusion Poisson process. Under the assurnptions that the claimsizes are subexponentially distributed and that the interest force is constant, we obtain an asymptotic formula for the finite-time ruin probability. The results we obtain extends the corresponding results of Kliippelberg and Stadtmüller and Tang.

Ruin probability of the renewal model with risky investment and large claims

The ruin probability of the renewal risk model with investment strategy for a capital market index is investigated in this paper.For claim sizes with common distribution of extended regular variation,we study the asymptotic behaviour of the ruin probability.As a corollary,we establish a simple asymptotic formula for the ruin probability for the case of Pareto-like claims.

Exponential Bounds for Ruin Probability in Two Moving Average Risk Models with Constant Interest Rate

The authors consider two discrete-time insurance risk models. Two moving average risk models are introduced to model the surplus process, and the probabilities of ruin are examined in models with a constant interest force. Exponential bounds for ruin probabilities of an infinite time horizon are derived by the martingale method.