OPTIMAL REINSURANCE UNDER EXPECTED VALUE PRINCIPLE

The paper concerns the problem how to purchase the reinsurance in order to make the insurer and the reinsurance company＇s total risk to be least under the expected value principle. When the insurer and reinsurance company take arbitrary risk measures, sufficient con- ditions for optimality of reinsurance contract are given within the restricted class of admissible contracts. Further, the explicit forms of optimal reinsurance contract under several special risk measures are given, and the method to decide parameters as well.

Estimating the expected value of multiple prospects in bidding blocks

In recent years,China has accelerated the reform of its oil and gas management system,especially in competitive transfer of mining rights.Evaluating the expected value(EV)of lease blocks is crucial for the bidding decision of oil companies.When bidding for a block with several individual prospects,the simple addition of each prospect EV usually leads to overly high and optimistic resource volume and value estimates.For the assessment of the EV of a multi-prospect block,two factors should be considered.Firstly,the geological setting of the prospects,including their relative spatial relationship,their chance of geological success,their resources and their geological dependency,etc.The second factor is the exploration strategy of oil companies,concerned with the dry hole tolerance,the committed wells and the drilling priorities for the prospects,etc.A probabilistic method to assess the EV of a multi-prospect block is proposed,which proves to be favorable for formulating a bidding strategy for oil companies.In addition,a case study on two specific blocks with several prospects is presented to illustrate the effect of the above mentioned factors on the EV.

Expected Value Method for Fuzzy Multiple Attribute Decision Making

This paper presents a fuzzy multiple attribute decision-making （FMADM） method in which the attribute weights and decision matrix elements （attribute values） are fuzzy variables. Fuzzy arithmetic and the expected value operator of fuzzy variables are used to develop the expected value method to solve the FMADM problem. A numerical example is given to demonstrate the feasibility and effectiveness of the method.

New Expected Value Expansions of Rooted Graphs

We propose a new expected value of rooted graph in this article,that is, when G is a rooted graph that each vertex may independently succeed with probability p when catastrophic thing happened, we consider the expected number of edges in the operational component of G which containing the root. And we get a very important and useful compute formula which is called deletion-contraction edge formula. By using this formula, we get the computational formulas of expected value for some special graphs. We also discuss the mean of expected value when parameter p has certain prior distribution. Finally, we propose mean-variance optimality when rooted graph has the equilibrium point which has larger mean and smaller variance.

On the Expected Present Value of Total Dividends in a Risk Model with Potentially Delayed Claims

In this paper, we consider a risk model in which two types of individual claims, main claims and by-claims, are defined. Every by-claim is induced by the main claim randomly and may be delayed for one time period with a certain probability. The dividend policy that certain amount of dividends will be paid as long as the surplus is greater than a constant dividend barrier is also introduced into this delayed claims risk model. By means of the probability generating functions, formulae for the expected present value of total dividend payments prior to ruin are obtained for discrete-type individual claims. Explicit expressions for the corresponding results are derived for K n claim amount distributions. Numerical illustrations are also given.

Does the EVA valuation model explain the market value of equity better under changing required return than constant required return?

Through the Economic-Value-Added(EVA)valuation model,the expected market value of equity can be determined by adding the book value of equity with the present value of expected EVAs under the assumption of constant required return and constant return on equity.The equation of EVA valuation model has taken its shape under the assumption of constant required return and constant return on equity.However,a large body of empirical evidence indicates that required rate of return never remain constant.The EVA-valuation model formulated under constant required return cannot be implemented under the scenario of changing required return.In this study,we explored whether the EVA valuation model could be implemented under changing required return by making any changes in the model and found that it could be implemented under the scenario of changing required return by replacing the book value of the equity of the existing model with the present value of required earnings or normal market earnings.We further examined whether the explanatory ability of the EVA valuation model under the assumption of changing required return is better than that of the valuation model under the assumption of constant required return.Relative information content analyses were conducted by considering sample of the intrinsic value of equities determined by valuation models and the market value of equities of 69 large-cap,88 mid-cap,and 79 small-cap companies.The results showed that the EVA-based valuation model with changing normal market return outperformed the EVA-based valuation model with constant required return.

Scheme to measure the expectation value of a physical quantity in weak coupling regime

In quantum mechanics, the expectation value of an operator can be measured by using the projective measurement, ifthe coupling between the measured system and pointer is strong enough. However in the weak coupling regime, the pointercan not show all the eigenvalue of the physical quantity directly due to the overlapping among the pointer states, whichmakes the measurement of the expectation value difficult. In this paper, we propose an expectation value measurementmethod in the weak coupling regime inspired by the weak measurement scheme. Compared to the projective measurement,our scheme has two obvious advantages. Experimentally we use the internal state and motional state of a single trapped40Ca+ to establish the measurement scheme and realize the proof of principle demonstration of the scheme.

A Note on the Expectation Value of Time

In this note, the expectation value of time based on quantum mechanics formalism is derived. It is found that the expectation value of time does not depend on space.

Behavioral Decision-Making of Key Stakeholders in Public-Private Partnerships:A Hybrid Method and Benefit Distribution Study

Public-private partnerships(PPPs)have been used by governments around the world to procure and construct infrastructural amenities.It relies on private sector expertise and funding to achieve this lofty objective.However,given the uncertainties of project management,transparency,accountability,and expropriation,this phenomenon has gained tremendous attention in recent years due to the important role it plays in curbing infrastructural deficits globally.Interestingly,the reasonable benefit distribution scheme in a PPP project is related to the behavior decisionmaking of the government and social capital,aswell as the performance of the project.In this paper,the government and social capital which are the key stakeholders of PPP projects were selected as the research objects.Based on the fuzzy expected value model and game theory,a hybrid method was adopted in this research taking into account the different risk preferences of both public entities and private parties under the fuzzy demand environment.To alleviate the problem of insufficient utilization of social capital in a PPP project,this paper seeks to grasp the relationship that exists between the benefit distribution of stakeholders,their behavioral decision-making,and project performance,given that they impact the performance of both public entities and private parties,as well as assist in maximizing the overall utility of the project.Furthermore,four game models were constructed in this study,while the expected value and opportunity-constrained programming model for optimal decision-making were derived using alternate perspectives of both centralized decision-making and decentralized decision-making.Afterward,the optimal behavioral decision-making of public entities and private parties in four scenarios was discussed and thereafter compared,which led to an ensuing discussion on the benefit distribution system under centralized decision-making.Lastly,based on an example case,the influence of different confidence levels,price,and fuzzy uncertainties of PPP projects on the equilibrium strategy results of both parties were discussed,giving credence to the effectiveness of the hybrid method.The results indicate that adjusting different confidence levels yields different equilibriumpoints,and therefore signposts that social capital has a fair perception of opportunities,as well as identifies reciprocal preferences.Nevertheless,we find that an increase in the cost coefficient of the government and social capital does not inhibit the effort of both parties.Our results also indicate that a reasonable benefit distribution of PPP projects can assist them in realizing optimum Pareto improvements over time.The results provide us with very useful strategies and recommendations to improve the overall performance of PPP projects in China.

LINEAR SEARCH FOR A BROWNIAN TARGET MOTION

A target is assumed to move according to a Brownian motion on the real line. The searcher starts from the origin and moves in the two directions from the starting point. The object is to detect the target. The purpose of this paper is to find the conditions under which the expected value of the first meeting time of the searcher and the target is finite, and to show the existence of a search plan which made this expected value minimum.

Fuzzy-entropy based robust optimization criteria for tuned mass dampers

Tuned mass dampers (TMD) are well known as one of the most widely adopted devices in vibration control passive strategies. In the past few decades,many methods have been developed to find the optimal parameters of a TMD installed on a structure and subjected to a random base excitation process,but most of them are usually based on an implicit assumption that all of the structural parameters are deterministic. However,in many real cases this simplification is unacceptable,so robust optimal design criteria becomes aviable alternative to better support engineers in the design process. In Robust Design Optimization (RDO) approaches,indeed the solution must be able to not only minimize the performance but also to limitits variation induced by uncertainty. Most of the currently available RDO methods are based on a probabilistic description of the model uncertainty,even if in many cases they are not able to explicitly include the influence of all the possible sources of uncertainties. Therefore,in this study,a fuzzy version of the robust TMD design optimization problem is proposed. The consistency of the fuzzy approach is studied with respect to the available non-probabilistic formulations reported in the literature and an application to an example of a robust design of a linear TMD subjected to base random vibrations in the presence of fuzzy uncertainties. The results show that the proposed fuzzy-based approach is able to give a set of optimal solutions both in terms of structural efficiency and sensitivity to mechanical and environmental uncertainties.

Ant Colony System for a Fuzzy Adjacent Multiple-Level Warehouse Layout Problem

A warehouse layout problem where the warehouse has more than one level and both the distance from the cell to the receive/exit bay and demand of item types are fuzzy variables is proposed. The problem is to find a layout with the minimum transportation cost subject to adjacency and other constraints. A fuzzy expected value model is given and an ant colony system is designed to solve the problem. Computational results indicate the efficiency and effectiveness of the method.

New approach for uncertain random multi-objective programming problems based on C_(ESD) criterion

To overcome the defects that the traditional ap-proach for multi-objective programming under uncertain ran-dom environment(URMOP)neglects the randomness and uncer-tainty of the problem and the volatility of the results,a new ap-proach is proposed based on expected value-standard devi-ation value criterion(C_(ESD) criterion).Firstly,the effective solution to the URMOP problem is defined;then,by applying sequence relationship between the uncertain random variables,the UR-MOP problem is transformed into a single-objective program-ming(SOP)under uncertain random environment(URSOP),which are transformed into a deterministic counterpart based on the C_(ESD) criterion.Then the validity of the new approach is proved that the optimal solution to the SOP problem is also effi-cient for the URMOP problem;finally,a numerical example and a case application are presented to show the effectiveness of the new approach.

Third Order Adjoint Sensitivity and Uncertainty Analysis of an OECD/NEA Reactor Physics Benchmark: III. Response Moments

The (180)3 third-order mixed sensitivities of the leakage response of a polyethylene-reflected plutonium (PERP) experimental benchmark with respect to the benchmark’s 180 microscopic total cross sections have been computed in accompanying works [1] [2]. This work quantifies the contributions of these (180)3 third-order mixed sensitivities to the PERP benchmark’s leakage response distribution moments (expected value, variance and skewness) and compares these contributions to those stemming from the corresponding first- and second-order sensitivities of the PERP benchmark’s leakage response with respect to the total cross sections. The numerical results obtained in this work reveal that the importance of the 3rd-order sensitivities can surpass the importance of the 1st- and 2nd-order sensitivities when the parameters’ uncertainties increase. In particular, for a uniform standard deviation of 10% of the microscopic total cross sections, the 3rd-order sensitivities contribute 80% to the response variance, whereas the contribution stemming from the 1st- and 2nd-order sensitivities amount only to 2% and 18%, respectively. Consequently, neglecting the 3rd-order sensitivities could cause a very large non-conservative error by under-reporting the response variance by a factor of 506%. The results obtained in this work also indicate that the effects of the 3rd-order sensitivities are to reduce the response’s skewness in parameter space, rendering the distribution of the leakage response more symmetric about its expected value. The results obtained in this work are the first such results ever published in reactor physics. Since correlations among the group-averaged microscopic total cross sections are not available, only the effects of typical standard deviations for these cross sections could be considered. Due to this lack of correlations among the cross sections, the effects of the mixed 3rd-order sensitivities could not be quantified exactly at this time. These effects could be quantified only when correlations among the group-averaged microscopic total cross sections would be obtained experimentally by the nuclear physics community.

Third-Order Adjoint Sensitivity Analysis of an OECD/NEA Reactor Physics Benchmark: I. Mathematical Framework

This work extends to third-order previously published work on developing the adjoint sensitivity and uncertainty analysis of the numerical model of a polyethylene-reflected plutonium (acronym: PERP) OECD/NEA reactor physics benchmark. The PERP benchmark comprises 21,976 imprecisely known (uncertain) model parameters. Previous works have used the adjoint sensitivity analysis methodology to compute exactly and efficiently all of the 21,976 first-order and (21,976)2 second-order sensitivities of the PERP benchmark’s leakage response to all of the benchmark’s uncertain parameters, showing that the largest and most consequential 1st- and 2nd-order response sensitivities are with respect to the total microscopic cross sections. These results have motivated extending the previous adjoint-based derivations to third-order, leading to the derivation, in this work, of the exact mathematical expressions of the (180)3 third-order sensitivities of the PERP leakage response with respect to these total microscopic cross sections. The formulas derived in this work are valid not only for the PERP benchmark but can also be used for computing the 3rd-order sensitivities of the leakage response of any nuclear system involving fissionable material and internal or external neutron sources. Subsequent works will use the adjoint-based mathematical expressions obtained in this work to compute exactly and efficiently the numerical values of these (180)3 third-order sensitivities (which turned out to be very large and consequential) and use them for a third-order uncertainty analysis of the PERP benchmark’s leakage response.

Quantitative Estimation of Experts’Judgments on Petroleum Exploration

A new method in making judgment matrix is proposed based on a basic value of “importance” and a relative measure level of “importance”. Factors affecting petroleum exploration are analyzed and Experts’ judgment matrix on a geologic formation is given. Expected value of each factor is computed and the volume of recoverable oil is estimated.

A Coordinated Search Algorithm for a Lost Target on the Plane

Concepts in search theory have developed since World War II.The study of search plans has found considerable interest among searchers due to its wide applications in our life.Searching for lost targets either located or moved is often a time-critical issue,especially when the target is very important.In many commercial and scientific missions at sea,it is of crucial importance to find lost targets underwater.We illustrate a technique known as coordinated search,that completely characterizes the search for a randomly located target on a plane.The idea is to avoid wasting time looking for a missing target.Two searchers or robots start from the center of a circle to search out a lost target,the first searcher looks for the target on the right side of the circular area,and the second one looks for it on the left side.The time taken to detect the target is obtained by assuming the target’s position has a symmetric distribution.The procedures to facilitate the detection of the target are presented as an algorithm and as a flow-chart.An application demonstrates the applicability of this search technique and the associated decrease in search cost.Its effectiveness is illustrated by numerical results,which indicates considerable promise.

An Ethical Approach to Decision Design

This paper describes an approach to ethical decision design. It discusses the use of several mathematical tools applicable to the world of economics and business. It then demonstrates how the tools analogously extend themselves to making ethical decisions as supported by personal values. A review of the mathematics, including the design of a decision tree, the concept of mathematical expectation, and mathematical modeling are included.

Charge density at the nucleus and radial behavior of ground state for lithium-like ions with Z=21 to 30

By using the full-core plus correlation （FCPC） type wave functions, the accurate charge densities p（0） at the nucleus and the radial expectation values of the ground states for the lithium-like systems with Z =- 21 to 30 are obtained. The determinantal conditions and the electron-nucleus cusp condition are used to calculate the inequalities of the upper and the lower bounds to p（0） with two or more expectation values. These inequalities, derived by Angulo and Dehesa [Phys. Rev. A 44 1516 （1991）], are verified to be also valid for these ions with higher nuclear charge. The present results show that the wave functions used in this paper are satisfactory in the whole configuration space for these ions with higher nuclear charge.

A Path Integral Generalization of Bell Local Hidden Variable Models for Unstable Particles

We discuss the problem of the generalization of Bell local hidden variable models for unstable particles as nucleons or decaying quantum bound states. We propose to extend the formalism of real deterministic hidden variables in the complex domain, in analogy with the quantum Gamow ket formalism, and we introduce a time dependent classical probability density distribution by which we implement hidden time dependence in the quantum expectation values. We suggest therefore a classical framework which may recover by asymptotic temporal limits the standard Bell stationary quantum statistical averages. Endly we discuss the possible relevance of our proposal for general non-isolated quantum systems in noninertial frames and the consequent dynamic effects of vacuum instabilities on E.P.R tests and Q.M. ensemble statistical averages.