Risk analysis in investment appraisal based on the Monte Carlo simulation technique by A. Hacura, M. Jadamus-Hacura and A. Kocot

Comment on Eur. Phys. J. B 20, 551 (2001) Since Hertz major work on investment appraisal using the Monte Carlo Simulation technique, the so called “Risk Analysis” has become a standard tool for supporting investment decisions [1,2]. A main problem in investment appraisal is to consider and specify the risk of investment projects in an appropriate way, for enabling consistent project evaluation. In calculating a risky project's net present value (NPV) the major difficulty is to quantify the project's risk for quantifying an appropriate risk adjusted discount rate (RADR). Theoretically not founded risk adjusted discount rates face a lot of critique. Furthermore it is discussed that the incorporation of a constant risk factor into the discount rate makes a certain assumption about the resolution of uncertainty over time [3] and finally that a single net present value could not in general reflect risk properly. Especially in consequence of the last point the proponents of simulation argue that a whole distribution of net present values shows a project's risk better than a single number. In the special issue “Econophysics” of this journal Hacura et al. tried to describe the methodology and use of Monte Carlo Simulation in investment appraisal [4]. The purpose of this comment is to point out three fundamental flaws in that article. Received 29 April 2002 Published online 19 December 2002 RID="a" ID="a"e-mail: robert.obermaier@wiwi.uni-regensburg.de     

A cluster Monte Carlo algorithm for 2-dimensional spin glasses

A new Monte Carlo algorithm for 2-dimensional spin glasses is presented. The use of clusters makes possible global updates and leads to a gain in speed of several orders of magnitude. As an example, we study the 2-dimensional ±J Edwards-Anderson model. The new algorithm allows us to equilibrate systems of size 100² down to temperature T = 0.1. Our main result is that the correlation length diverges as an exponential ( ξ∼e ^2βJ) and not as a power law as T↦T _c = 0. Received 10 January 2001 and Received in final form 29 May 2001     

Monte Carlo calculations of angular momentum projected many-body matrix elements in the Pairing Plus Quadrupole Model

We extend the recently presented formalism for Monte Carlo calculations of the partition function, for both even and odd particle number systems (Phys. Rev. C 59, 2500 (1999)), to the calculation of many-body matrix elements of the type <ψ| e ^{- βℋ}|ψ> where |ψ> is a many-body state with a definite angular momentum, parity, neutron and proton numbers. For large β such matrix elements are dominated by the lowest eigenstate of the many-body Hamiltonian ℋ, corresponding with a given angular momentum parity and particle number. Emphasis is placed on odd-mass nuclei. Negligible sign fluctuations in the Monte Carlo calculation are found provided the neutron and proton chemical potentials are properly adjusted. The formalism is applied to the J ^π = 0⁺ state in ¹⁶⁶ Er and to the J ^π = 9/2^-, 13/2⁺, 5/2^- states in ¹⁶⁵ Er using the pairing-plus-quadrupole model. Received: 28 April 2000 / Accepted: 20 September 2000     

Molecular structure calculations via path integral simulations: Estimating finite-discretization errors

Path integral simulations are now recognized as a useful tool to determine theoretically the structure of complex molecules at finite temperatures including quantum effects. In addition to statistical errors due to incomplete sampling, also systematic errors are inherent in this procedure because of the finite discretization of the path integral. Here, useful “back of the envelope” estimates to assess the systematic errors of bond-length distribution functions are introduced. These analytical estimates are tested for two small molecules, HD⁺ and H₃ ⁺, where quasi-exact benchmark data are available. The accuracy of the formulae is shown to be sufficient in order to allow for a reliable assessment of the quality of the discretization in a given simulation. The estimates will also be applicable in condensed phase path integral simulations, and the basic idea can be generalized to other observables than those presented. Received 13 September 1999 and Received in final form 18 November 1999     

Optimized Monte Carlo analysis for generalized ensembles

We present a new, maximum-likelihood based method to combine data from a multiple number of Monte Carlo simulations performed within any type of ensemble. The method offers an efficient iterative scheme to obtain the density of states of a wide range of energies as well as of other macroscopic variables. It should in particular be useful for the study of systems with a rough energy landscape. Received 4 June 2002 Published online 14 October 2002 RID="a" ID="a"e-mail: borg@alf.nbi.dk     

Effect of eugenics on the evolution of populations

We discuss a model of population dynamics under selection pressure from a changing environment. The population, subject to mutations, is composed of diploidal organisms reproducing quasi-sexually (two parents, recombination but no sexes) and with overlapping generations. Two cases are considered - in one we do not influence the dynamics of the population, while in the other we perform eugenics, i.e. we eliminate all individuals which have phenotypes not conforming to the optimal one at the place where the change has been made. We show that eugenics reduces greatly genetic diversity of the population, increases the percentage of homozygotes and therefore leads to a population badly prepared to cope with the next changes of the environment. The present paper is an extension of our previous work (Ref. [9]). Received 16 May 2000     

Monte Carlo method for neutron spectrum recovery - a new approach based on the accelerated ions distribution

New method of neutron spectrum recovery described in the paper involves accelerated deuterons (that produce neutrons in DD reaction) and allows getting neutron spectrum in any direction from computed time-velocity characteristics of deuterons. Time of flight signals registered in various distances and directions are used, that makes information involved in the recovery process (Monte-Carlo simulation) more complete than in a one-directional case, although additional assumption about axial symmetry of deuterons motion, is required. In the paper recent results of two standard tests of the proposed method are presented demonstrating its capability to recover neutron spectrum from time-of-flight signals.     

Heisenberg picture operators in the stochastic wave function approach to open quantum systems

A fast simulation algorithm for the calculation of multitime correlation functions of open quantum systems is presented. It is demonstrated that any stochastic process which “unravels” the quantum Master equation can be used for the calculation of matrix elements of reduced Heisenberg picture operators, and thus for the calculation of multitime correlation functions, by extending the stochastic process to a doubled Hilbert space. The numerical performance of the stochastic simulation algorithm is investigated by means of a standard example. Received: 30 May 1997 / Revised: 4 November 1997 / Accepted: 7 November 1997     

Slowing down in the three-dimensional three-state Potts glass with nearest neighbor exchange ± J: A Monte Carlo study

,Static and dynamic properties of the Potts model on the simple cubic lattice with nearest neighbor -interaction are obtained from Monte Carlo simulations in a temperature range where full thermal equilibrium still can be achieved (). For a lattice size L = 16, in this range finite size effects are still negligible, but the data for the spin glass susceptibility agree with previous extrapolations based on finite size scaling of very small lattices. While the static properties are compatible with a zero temperature transition, they certainly do not prove it. Unlike the Ising spin glass, the decay of the time-dependent order parameter is compatible with a simple Kohlrausch function, , while a power law prefactor cannot be distinguished. The Kohlrausch exponent y ( T ) decreases from at [0pt] to at [0pt] however. The relaxation time is compatible with the exponential divergence postulated by McMillan for spin glasses at their lower critical dimension, but the exponent that can be extracted still differs significantly from the theoretical value, . Thus the present results support the conclusion that the Potts spin glass in d = 3 dimensions differs qualitatively from the Ising spin glass. Received: 8 October 1997 / Accepted: 27 November 1997     

Influence of the Brownian step size in off-lattice Monte Carlo simulations of irreversible particle aggregation

The influence of the Brownian step size in off-lattice Monte Carlo simulations of the aggregation and gelation of spheres is studied. It is found that the kinetics are strongly influenced if the step size is larger than the mean smallest distance between the sphere surfaces. The structure of the clusters and the gels is influenced, but only over length scales smaller than the step size. Using large step sizes leads to a narrower size distribution of the clusters. Implications of the present results are discussed for simulations reported in the literature in which the Brownian step size was chosen equal to the sphere diameter.     

Attractive forces between anisotropic inclusions in the membrane of a vesicle

The fluctuation-induced interaction between two rod-like, rigid inclusions in a fluid vesicle is studied by means of canonical ensemble Monte-Carlo simulations. The vesicle membrane is represented by a triangulated network of hard spheres. Five rigidly connected hard spheres form rod-like inclusions that can leap between sites of the triangular network. Their effective interaction potential is computed as a function of mutual distance and angle of the inclusions. On account of the hard-core potential among these, the nature of the potential is purely entropic. Special precaution is taken to reduce lattice artifacts and the influence of finite-size effects due to the spherical geometry. Our results show that the effective potential is attractive and short-range compared with the rod length L. Its well depth is of the order of , where is the bending modulus. Received 5 February 1999 and Received in final form 14 May 1999     

Weakly nonextensive thermostatistics and the Ising model with long-range interactions

We introduce a new nonextensive entropic measure that grows like , where N is the size of the system under consideration. This kind of nonextensivity arises in a natural way in some N-body systems endowed with long-range interactions described by interparticle potentials. The power law (weakly nonextensive) behavior exhibited by is intermediate between (1) the linear (extensive) regime characterizing the standard Boltzmann-Gibbs entropy and (2) the exponential law (strongly nonextensive) behavior associated with the Tsallis generalized q-entropies. The functional is parametrized by the real number in such a way that the standard logarithmic entropy is recovered when . We study the mathematical properties of the new entropy, showing that the basic requirements for a well behaved entropy functional are verified, i.e., possesses the usual properties of positivity, equiprobability, concavity and irreversibility and verifies Khinchin axioms except the one related to additivity since is nonextensive. For , the entropy becomes superadditive in the thermodynamic limit. The present formalism is illustrated by a numerical study of the thermodynamic scaling laws of a ferromagnetic Ising model with long-range interactions. Received 24 May 2000     

Monte Carlo法模拟油滴的理论分布

在密立根油滴实验中,应用Monte Carlo法数值地模拟实验室条件下可能的油滴带电量Q、平衡电压U和匀速运动时间t的理论分布,分别从三维分布、时间分布及数量方面比较3种选择油滴的标准,给出较合理的结论.     

热辐射输运问题的高效蒙特卡罗模拟方法

惯性约束聚变研究中,热辐射光子在介质中的输运以及热辐射光子与介质的相互作用是重要研究课题,蒙特卡罗方法是该类问题的重要研究手段之一.隐式蒙特卡罗方法虽然能正确地模拟热辐射在介质中的输运过程,但当模拟重介质(材料的吸收系数大)问题时,该方法花费的计算时间将变得很长,导致模拟效率很低.本文以离散扩散蒙特卡罗方法为基础,开发了"离散扩散蒙特卡罗方法辐射输运模拟程序",可以较好地解决重介质区的计算效率问题,但是离散扩散蒙卡罗方法在模拟轻介质区时精度不够高.辐射输运问题中通常既有轻介质也有重介质,为了能同时解决蒙特卡罗方法模拟的效率和精度问题,本文研究了离散扩散蒙特卡罗方法与隐式蒙特卡罗方法相结合的模拟方法,并提出了新的扩散区与输运区界面处理方法,研制了混合蒙特卡罗方法的辐射输运模拟程序.典型辐射输运问题模拟显示:在模拟重介质问题时,该程序能大幅缩短模拟时间,且能取得与隐式蒙特卡罗方法一致的结果;在模拟轻重介质均存在的问题时,与隐式蒙特卡罗方法相比,混合蒙特卡罗方法的模拟精度与其相当且计算效率同样能够得到显著提升.     

A new simulation method for the determination of forces in polymer/colloid systems

We introduce a new simulation method, which we call the contact-distribution method, for the determination of the Helmholtz potential for polymer/colloid systems from lattice Monte-Carlo simulations. This method allows one to obtain forces between finite or semi-infinite objects of any arbitrary shape and dimensions in the presence of polymer chains in solution or physisorbed or chemisorbed at interfaces. We illustrate the application of the method using two examples: (i) the interaction between the tip of an atomic force microscope (AFM) and a single, end-grafted polymer chain and (ii) the interaction between an AFM tip and a polymer brush. Numerical results for the first two cases illustrate how the method can be used to confirm and extend scaling laws for forces and Helmholtz potentials, to examine the effects of the shapes and sizes of the objects and to examine conformational transitions in the polymer chains. Received: 15 May 1998 / Revised: 11 June 1998 / Accepted: 12 June 1998     

Crystallization and quantum melting of few electron system in a spherical quantum dot: quantum Monte Carlo simulation

Spherical quantum dots with a few charged Fermi particles (electrons or holes) are studied for different total spins. Simulation by quantum path integral Monte Carlo method is performed. The dependence of the electron correlations in the quantum dot is studied at different mean interelectron separation controlled by number of electrons in the quantum dot and by steepness of electron confinement (the latter parameter can be changed by the gate voltage). The ‘cold’ melting—quantum transition from Wigner crystal-like state (i.e. from regime of strongly correlated electrons) to a Fermi liquid-like state—driven by the steepness of electron confinement is studied. The pair correlation function and radial function characterizing electron quantum delocalization are analyzed.     

Monte Carlo simulation using the Fourier transform of the interatomic potential

When doing Monte Carlo simulations using continuous potentials, the evaluation of the configurational potential energy ink-space by Fourier transformation is shown to be a computationally attractive scheme for systems where the long-range interatomic interaction spans a dimension comparable to the size of the simulated system.     

基于蒙特卡罗方法的中子屏蔽材料设计

基于蒙特卡罗粒子输运程序MCNP,设计了一种强度高、密度低、具有优异中子屏蔽性能的新型玻璃纤维/B4C/环氧树脂复合材料,模拟计算了镅-铍（Am-Be）中子源产生中子对该材料的透射率;研究了该材料的中子屏蔽性能与传统屏蔽材料的差异以及不同B4C质量分数对该材料的屏蔽性能影响;根据模拟结果分析了该材料对不同能区中子（慢中子、中能中子、快中子）具有的不同屏蔽性能。研究发现：B4C质量分数为10%的该种新型玻璃纤维/B4C/环氧树脂复合材料的中子屏蔽性能,尤其是慢中子屏蔽性能较传统的含硼聚乙烯和Al-B4C合金材料更为优异;但随着B4C质量分数的增大,屏蔽性能提升不明显。结果验证了蒙特卡罗方法用于中子屏蔽材料优化设计的可行性。     

Monte-Carlo analysis of tracer diffusion mechanisms in YBa2Cu3O6+c

A method for estimating, via the Monte-Carlo simulation, the most often realized diffusion mechanisms in 2D ordered structures is presented. Taking as an example the diffusion of oxygen ions in high temperature superconductor we propose several diffusion mechanisms and show to what extent they depend on the temperature and concentration of the diffusing particles. Our results are compared with the ones proposed earlier on the basis of energy arguments. We find also additional trajectories, different from those earlier reported in that system. Received 9 November 1998     

Model of population evolution with and without eugenics

We propose, and solve via Monte-Carlo simulation, a model describing evolution of population subject to harmful mutations. The habitat changes periodically. The evolution of two, initially identical, populations is compared. One without any external ingerence and the second in which we eliminate all individuals which are ill-fitted to the changed environment (eugenics). We show that although in the short run the individuals in the latter are better adapted and live longer, after some more changes of the environment, the populations with eugenics become extinct, while the others live on. Received 8 April 1999