一个修正的PVT算法

对Fkshima(1998）所提出的PVT算法给出一种修正算法，称为修正PVT算法，这一修正算法对PVT原算法中的并行步中的停止准则和同步步骤作了修正。修正PVT算法的停止条件对PVT原算法的停止条件弱，因此更适用于并行计算，并且计算时间比PVT原算法少。     

求解隐式迭代方程的多尺度配置法

用多尺度快速配置法求解病态积分方程的隐式迭代方程.在积分算子是扇形紧算子时,该方法得到了离散隐式迭代方程的近似解.采用Morozov偏差原理作为停止准则,并证明了在该准则下隐式迭代正则化方法所得近似解的收敛率.最后,用数值实验证实理论结果和说明数值方法的有效性.     

求解非定常Lavrentiev迭代方程的多尺度配置法

本文采用多尺度配置法求解第一类弱扇形积分方程.将压缩配置法用于投影离散非定常迭代正则化方程,得到了近似解在Banach空间范数下误差估计,给出了迭代停止准则,确保近似解无穷范数下的最优收敛率.优点是确保了收敛率,减少了计算量.数值例子验证了算法的有效性.     

基于追溯保费原理的最优再保险策略

追溯保费是一种依赖于保单期保险人实际损失的保费厘定计划,是对过去已经发生的损失进行承保的保险方式.本文将追溯保费应用于再保险模型中,当最优准则选为最小化风险调整值而风险资本用TVaR来度量时,得到的最优分保函数形式为停止损失再保险.进而,研究了最优停止损失再保险中最优自留额的求解算法.最后,假设损失服从指数分布、Pareto分布和Gamma分布等情形,利用数值举例的方法研究了税租乘数T和安全负荷系数ρ对最优自留额和最小风险调整值的影响.结果表明,当其他参数一定时, T增大,最优自留额增大而最小风险调整值减小;而其他参数一定时,最优自留额和最小风险调整值都会随着ρ的增大而增大.     

信息复杂性准则的深入探讨

介绍联系拟合优度与模型复杂性测度的一种模型选择准则一信息复杂性(ICOMP)准则的基本原理.由Bozdogan提出的信息复杂性(ICOMP)准则可以视为两个Kullback-Leibler距离之和的一种近似.首先研究了所考虑模型中有真实模型的情况下,ICOMP准则类的渐近相容性;然后又介绍并完成了所考虑模型中没有真实模型的情况下,ICOMP准则类的渐近相容性.在有限样本容量的情况下,用ICOMP准则选择的估计模型,比用其他通用的准则选择的估计模型,更接近于真实模型.     

关于交错级数的审敛准则的改进和推广

讨论了交错级数的敛散性,改进了[1]中关于交错级数新的审敛准则,并给出了交错级数另外新的审敛准则,并将这些审敛准则推广到更一般的形式.     

预测复合材料开裂方向的比应变能密度准则

本文提出预测复合材料中裂纹方向的比应变能密度准则,并将Tsai-Hill与Norris准则扩展来预测复合材料中的开裂方向.用这三个准则预测了具有各种不同纤维方向的单向纤维复合材料的裂纹扩展方向,预测结果与现有的比正应力准则和应变能密度准则进行了对比.     

Orlicz空间的近端点和近严格凸性

本文给出了Orlicz函数空间中近端点的判别准则,近而推出了Orlicz函数空目近严格凸性的判别准则.另外,本文还直接给出Orlicz序列空间近严格凸的判别准则.     

Panel模型中常见估计的比较

本文研究了Panel模型中回归系数常见估计的比较问题,给出了在Pitman准则,协方差阵准则和广义均方误差准则下最小二乘估计,Within估计,Between估计及两步估计之间的优良性比较结果.特别地,本文证明了在Pitman准则下最小二乘估计一致地优于Between估计.     

Gauss因果模型中因果效应识别方法的比较

一个Gauss因果模型中常常存在不只一种识别因果效应的方法, 不同的方法对应的估计可能不同. 该文对Pearl等人提出的前门准则, 后门准则,工具变量准则等识别方法的估计精度进行了分析比较, 并给出了相应的模拟结果, 为实践中选择更优的识别准则提供了依据.     

A general steady state distribution based stopping criteria for finite length genetic algorithms

We propose two general stopping criteria for finite length, simple genetic algorithms based on steady state distributions, and empirically investigate the impact of mutation rate, string length, crossover rate and population size on their convergence. Our first stopping criterion is based on the second largest eigenvalue of the genetic algorithm transition matrix, and the second stopping criterion is based on minorization conditions.     

Solving nonlinear simultaneous equations with a generalization of Brent's method

We describe an implementation of a generalization of Brent's method for solving systems of nonlinear equations. Some important features of the algorithm, like step control, discretization of derivatives and stopping criteria, are discussed. In particular we give numerical experiences which show that a stopping criterion proposed by D. Gay is efficient.     

An improved numerical method for balanced truncation for symmetric second-order systems

We consider balanced truncation model order reduction for symmetric second-order systems. The occurring large-scale generalized and structured Lyapunov equations are solved with a specially adapted low-rank alternating directions implicit (ADI) type method. Stopping criteria for this iteration are investigated, and a new result concerning the Lyapunov residual within the low-rank ADI method is established. We also propose a goal-oriented stopping criterion which tries to incorporate the balanced truncation approach already during the ADI iteration. The model reduction approach using the ADI method with different stopping criteria is evaluated on several test systems.     

Stopping criteria for inner iterations in inexact potential reduction methods: a computational study

We focus on the use of adaptive stopping criteria in iterative methods for KKT systems that arise in Potential Reduction methods for quadratic programming. The aim of these criteria is to relate the accuracy in the solution of the KKT system to the quality of the current iterate, to get computational efficiency. We analyze a stopping criterion deriving from the convergence theory of inexact Potential Reduction methods and investigate the possibility of relaxing it in order to reduce as much as possible the overall computational cost. We also devise computational strategies to face a possible slowdown of convergence when an insufficient accuracy is required.     

Extreme events,discounting and stochastic optimization

The paper analyzes the implications of extreme events on the proper choice of discounting. Any discounting with constant or declining rates can be linked to random “stopping time” events, which define the internal discount-related horizons of evaluations. Conversely, any stopping time induces a discounting, in particular, with the standard discount rates. The expected duration of the stopping time horizon for discount rates obtained from capital markets does not exceed a few decades and, as such, these rates may significantly underestimate the net benefits of long-term decisions. The alternative undiscounted stopping time criterion allows to induce social discounting focusing on arrival times of potential extreme events rather then horizons of market interests. Induced discount rates are conditional on the degree of social commitment to mitigate risk. In general, extreme events affect these rates, which alter the optimal mitigation efforts that, in turn, change events. The use of undiscounted stopping time criteria requires stochastic optimisation methods.     

Alternative optimality criteria of portfolio selection based upon threshold stopping rule

This paper proposes two types of alternative criteria of optimality for the continuous time portfolio selection problem. The optimality criteria, the so–called Laplace–Stieltjes transform (LST) criteria, are based on the assumption that the financial agent has a target level for the wealth accumulation process. These criteria are closely related to the so–called threshold stopping investment rule. We analytically derive the LST criteria and numerically compare them with the well–known Kelly criterion. It is shown that the portfolio strategies suggested may overcome the problem that the growth portfolio is often overestimated in several investment situations.     

Stopping times for quantum Markov chains

In the paper we introduce stopping times for quantum Markov states. We study algebras and maps corresponding to stopping times, give a condition of strong Markov property and give classification of projections for the property of accessibility. Our main result is a new recurrence criterium in terms of stopping times (Theorem 1 and Corollary 2). As an application of the criterium we study how, in Section 6, the quantum Markov chain associated with the one-dimensional Heisenberg (usually non-Markovian) process, obtained from this quantum Markov chain by restriction to a diagonal subalgebra, is such that all its states are recurrent. We were not able to obtain this result from the known recurrence criteria of classical probability.Supported by GNAFA-CNR, Bando n. 211.01.25.     

Selection of a correlated equilibrium in Markov stopping games

This paper deals with an extension of the concept of correlated strategies to Markov stopping games. The Nash equilibrium approach to solving nonzero-sum stopping games may give multiple solutions. An arbitrator can suggest to each player the decision to be applied at each stage based on a joint distribution over the players’ decisions according to some optimality criterion. This is a form of equilibrium selection. Examples of correlated equilibria in nonzero-sum games related to the best choice problem are given. Several concepts of criteria for selecting a correlated equilibrium are used.     

Iteratively regularized Gauss–Newton method for operator equations with normally solvable derivative at the solution

We study the iteratively regularized Gauss–Newton method in a Hilbert space for solving irregular nonlinear equations with smooth operators having normally solvable derivatives at the solution. We consider both a priori and a posteriori stopping criteria for the iterations and establish accuracy estimates for resulting approximations. In the case where the a priori stopping rule is used, the accuracy of approximations arises to be proportional to the error level in input data. The latter result generalizes well-known estimates of this kind obtained for linear equations with normally solvable operators.