EXPECTED DISCOUNTED PENALTY FUNCTION OF ERLANG(2) RISK MODEL WITH CONSTANT INTEREST

The purpose of this paper is to consider the expected value of a discounted penalty due at ruin in the Erlang（2） risk process under constant interest force. An integro-differential equation satisfied by the expected value and a second-order differential equation for the Laplace transform of the expected value are derived. In addition, the paper will present the recursive algorithm for the joint distribution of the surplus immediately before ruin and the deficit at ruin. Finally, by the differential equation, the defective renewal equation and the explicit expression for the expected value are given in the interest-free case.

Intracerebral interplay and neurotransmitter systems involvement in animal models of neurodegenerative disorders:EEG approach expectations

An imbalance between activities of different structures and neurotransmitter systems in the brain is suggested to be the main cause of its abnormal functioning in neurodegenerative pathologies.Electroencephalogram（EEG）registered from areas specifically linked with a disease in combination with pharmacological testing of involved mediatory systems allows discovery of its progression and mechanism（s）. This, in turn, potentiates development of perspective approaches for early diagnostic and effective treatment of neurodegenerative disorders.

On the Expected Discounted Penalty Function for a Risk Process with Stochastic Return on Investments

This paper considers the expected discounted penalty function Φ（u） for the perturbed compound Poisson risk model with stochastic return on investments. After presenting an integro-differential equation that the expected discounted penalty function satisfies, the paper derives the closed form solution by constructing an identical equation. The exact expression for Φ （0） is given using the Laplace transform technique when interest rate is constant. Applications of the results are given to the ruin probability and moments of the deficit at ruin.

Some Statistical Properties of the Correlation Function of Combination Sequences

in this paper,the statistical prOPerties of random combination sequences are discussed.Thevalue of E{R(r)}and the upper bound of E{A(r)}are derived.In the end,a new method to find a longsequence with low autocorrelation value is given.

Dividend-Reinsurance Strategy in the Sparre Andersen Model

In this paper, we introduce a reinsurance strategy into the Sparre Andersen risk model with a horizon dividend barrier, which is named dividend-reinsurance strategy. It is shown that the value function of the new strategy far exceeds that of the optimal barrier strategy （even that of the optimal dividend strategy）. Some results on the advantages of the new strategy are obtained, and the methods for computing the value functions are provided. Numerical illustrations for Erlang （2） and compound Poisson risk models are also given.

A Note on the Perturbed Compound Poisson Risk Model with a Threshold Dividend Strategy

In this paper, we consider the Perturbed Compound Poisson Risk Model with a threshold dividend strategy （PCT）. Integro-differential equations （IDE） for its Cerber-Shiu functions and dividend payments function are stated. We maily focus on deriving the boundary conditions to solve these equations.