Analysis of Optimal Portfolio with Different Utility Function

The question of optimal portfolio is that finds the trading strategy satisfying the maximal expected utility function subject to some constraints. There is the optimal trading strategy under the risk neutral probability measure （martingale measure） if and only if there is no-arbitrage opportunity in the market. This paper argues the optimal wealth and the optimal value of expected utility with different utility function.

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.

The Gerber-Shiu Expected Discounted Penalty Function for Lévy Insurance Risk Processes

In this paper,we study a general Lévy risk process with positive and negative jumps.A renewal equation and an infinite series expression are obtained for the expected discounted penalty function of this risk model.We also examine some asymptotic behaviors for the ruin probability as the initial capital tends to infinity.

A Ruin Model with Random Income and Dependence between Claim Sizes and Claim Intervals

In this paper,we consider a generalization of the classical ruin model,where the income is random and the distribution of the time between two claim occurrences depends on the previous claim size.This model is more appropriate than the classical ruin model.Explicit expression for the generating function of the Gerber-Shiu expected discounted penalty function are derived.A similar model is discussed.Finally,the result are showed by two examples.

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.

Image reconstruction of a neutron scatter camera

Recently, Sandia Laboratories developed a neutron scatter camera to detect special nuclear materials. This camera exhibits the following advantages: high efficiency, direction discrimination, neutron-gamma discrimination ability, and wide field of view. However, using the direct projection method, the angular resolution of this camera is limited by uncertainties in the energies estimated from pulse height and time of flight measurements. In this study, we established an eight-element neutron scatter camera and conducted the experiment with a ^(252)Cf neutron source. The results show that it has an angular resolution better than 8°(1s) and a detection efficiency of approximately 2.6′10-4. Using maximum likelihood expectation maximization method, the image artifact was eliminated, and the angular resolution was improved. We proposed an average scattering angle method to estimate the scattering energy of neutrons and Compton gamma rays. As such, we can obtain a recognizable image and energy spectrum of the source with some degradation of energy and image resolutions. Finally, a newly measured light response function based on the MPD^(-4) device was used for image reconstruction. Although we did not obtain a better result than that of the standard light response function, we have observed the effects of light response function on image reconstruction.