Ruin probabilities with random rates of interest

A model was proposed for addressing investment risk of the flee reserve in the form of credit or currency risk. This risk was expressed by a constant amount K （ e. g., securitization） upon an interest-increasing event and a random variable Z representing the recovery rate of a bond or a devaluation factor. The model equation is an integro-differential equation with deviating arguments. The analytical solutions were obtained for the probability of survival as Z is a discrete random variable and as Z is a continuous random variable respectively.

On the Distribution of Duration of First Negative Surplus for a Discrete Time Risk Model with Random Interest Rate

In this paper, we examine further annuity-due risk model presented by Cai （Probability in the Engineering and Informational Sciences, 16（2002）, 309-324）. We consider the computation for the distribution of duration of first negative surplus and the algorithm is shown for calculating probability that ruin occurs and the duration of first negative surplus takes any nonnegative integers values. Numerical illustration for the main result is given.

UNIFORM ESTIMATE ON FINITE TIME RUIN PROBABILITIES WITH RANDOM INTEREST RATE

We consider a discrete time risk model in which the net payout （insurance risk） {Xk, k = 1, 2,...} are assumed to take real values and belong to the heavy-tailed class L∩ D and the discount factors （financial risk） {Yk, k = 1,2,...} concentrate on [θ, L], where 0 〈 0 〈 1, L 〈 ∞, {Xk, k = 1,2,...}, and {Yk, k=1,2,...} are assumed to be mutually independent. We investigate the asymptotic behavior of the ruin probability within a finite time horizon as the initial capital tends to infinity, and figure out that the convergence holds uniformly for all n ≥ 1, which is different from Tang Q H and Tsitsiashvili G （Adv Appl Prob, 2004, 36： 1278-1299）.

Quick System-Level DDR3 Signal Integrity Simulation Research

Double data rate synchronous dynamic random access memory （DDR3） has become one of the most mainstream applications in current server and computer systems. In order to quickly set up a system-level signal integrity （SI） simulation flow for the DDR3 interface, two system-level SI simulation methodologies, which are board-level S-parameter extraction in the frequency-domain and system-level simulation assumptions in the time domain, are introduced in this paper. By comparing the flow of Speed2000 and PowerSI/Hspice, PowerSI is chosen for the printed circuit board （PCB） board-level S-parameter extraction, while Tektronix oscilloscope （TDS7404） is used for the DDR3 waveform measurement. The lab measurement shows good agreement between simulation and measurement. The study shows that the combination of PowerSI and Hspice is recommended for quick system-level DDR3 SI simulation.

Phase transition for SIR model with random transition rates on complete graphs

We are concerned with the susceptible-infective-removed （SIR） model with random transition rates on complete graphs Cn with n vertices. We assign independent and identically distributed （i.i.d.） copies of a positive random variable ξ on each vertex as the recovery rates and i.i.d, copies of a positive random variable ρ on each edge as the edge infection weights. We assume that a susceptible vertex is infected by an infective one at rate proportional to the edge weight on the edge connecting these two vertices while an infective vertex becomes removed with rate equals the recovery rate on it, then we show that the model performs the following phase transition when at t = 0 one vertex is infective and others are susceptible. There exists λc 〉 0 such that when λ 〈 λc, the proportion r∞ of vertices which have ever been infective converges to 0 weakly as n → ＋∞ while when λ 〉 λc, there exist c（λ） 〉 0 and b（λ） 〉 0 such that for each n ≥ 1 with probability p ≥ b（λ）, the proportion r∞ ≥ c（λ）. Furthermore, we prove that Ac is the inverse of the production of the mean of p and the mean of the inverse of ξ.