A Fuzzy Stopping Problem with the Concept

Stimulated by Zadeh's paper (Journal of Statistical Planning and Inference,2002, 105, 233--264), we will try to consider a perceptive analysis of the optimal stopping problem. In this paper, the fuzzy perception value of the expectation of the optimal stopped reward is characterized and calculated by a new recursive equation. Also, a numerical example described by triangular fuzzy numbers is given.     

Invariant Boundary‐Value Problems of an Optimally Controlled Boundary Layer

The group properties of equations of the variational problem on finding a continuous law for velocity distribution of liquid injection into an incompressible laminar boundary layer in a planar case, which ensures the minimum friction force acting on the airfoil, are considered. It is shown that the optimal injection velocity on a wedge with x=0 is finite.     

A strong variational algorithm for delay systems

In this paper, we present a convergent extension of the first-order strong-variational algorithm by Mayne and Polak (Ref. 1) for solving optimal control problems with control constraints to delay systems. Although the algorithm is similar to the one presented in Ref. 1, the proof of convergence is different, since the differential dynamic techniques used by Mayne and Polak are not applicable.This work forms part of the author's PhD Dissertation and was conducted at the Imperial College of Science and Technology under a studentship awarded by the UK Science and Engineering Research Council. This assistance is gratefully acknowledged. The author also wishes to thank Dr. R. B. Vinter for his encouragement and help.     

极端嗜盐菌冻干保藏及其质检稳定性的研究

采用优化组合保护剂冷冻干燥２０株极端嗜盐菌，于４℃冷库保存２年，经复水测定，全部菌株保持较高存活性．用ＴＥＮＳ法对其中９株菌Ｒ１，ＲＦ１，Ｊ７，Ｓ９，Ｔ４～１，Ｊ６，Ｒ６～１，Ｒ６～７和Ｒ６～５作质粒稳定性检测，含质粒的菌株ＲＦ１，Ｊ７，Ｓ９，Ｔ４～１，Ｒ６～５于４℃保存２年后，质粒稳定存在；而菌株Ｒ１，Ｊ８，Ｒ６～１和Ｒ６～７冻干保存前后均末检测到质粒．结果表明：优化组合保护剂不仅能有效地用于极端嗜盐菌的冷冻干燥保藏，还能保持宿主质粒的稳定性．     

Transversality condition for infinite-horizon problems

We present necessary conditions of optimality for an infinitehorizon optimal control problem. The transversality condition is derived with the help of stability theory and is formulated in terms of the Lyapunov exponents of solutions to the adjoint equation. A problem without an exponential factor in the integral functional is considered. Necessary and sufficient conditions of optimality are proved for linear quadratic problems with conelike control constraints.     

Another Jacobi sufficiency criterion for optimal control with smooth constraints

In order to tighten the gap between necessary and sufficient conditions, new second-order sufficient conditions are developed for optimal control problems, where the control set is given by smooth functions. When the control set is polyhedral, our criterion generalizes prior results of the same kind, namely, the Jacobi criterion in Hamiltonian form and that in Lagrangian form (Refs. 1–3).The research of V. Zeidan was supported by NSERC Grant A-8570, which is gratefully acknowledged.     

Investors’ preference for a positive tax rate depends on the level of the interest rate

In a financial market with only one stock, Cadenillas and Pliska (Financ Stoch 3:137–165, 1999) showed that sometimes investors can take advantage of a positive tax rate to maximize their portfolio return. Buescu et al. (Math Finance 17:477–485, 2007) generalized this surprising result to a market with one stock and one bank account with zero interest rate. We consider instead a financial market with one stock and one bank account with positive interest rate. As in the papers above, we assume that there are taxes and transaction costs in the financial market. We succeed in solving the problem of an investor who wants to maximize the long-run growth rate of his investment, even though the positivity of the interest rate increases the dimensionality of the problem and the difficulty of the computations. We characterize how the investors’ preference for a positive tax rate depends on the interest rate level: investors prefer a positive tax rate when the level of the interest rate is low, and the opposite occurs when the level of the interest rate is high. Most of the contributions of C. Buescu were made during his doctoral studies at the University of Alberta. The research of C. Buescu and A. Cadenillas was supported by the Social Sciences and Humanities Research Council of Canada grants 410-2003-1401 and 410-2006-1069. We are grateful to Stanley R. Pliska for comments and suggestions to a previous version of the paper, and to the associate editor and referees for constructive remarks. Existing errors are our sole responsibility.     

Testing the Gumbel Hypothesis Via the Pot-Method

We consider an i.i.d. sample, generated by some distribution function, which belongs to the domain of attraction of an extreme value distribution with unknown shape and scale parameters. We treat the scale parameter as a nuisance parameter and establish for the hypothesis of Gumbel domain of attraction an asymptotically optimal test based on those observations among the sample, which exceed a given threshold sequence. Asymptotic optimality is achieved along certain contiguous extreme value alternatives within the concept of local asymptotic normality (LAN). Adaptive test procedures exist under restrictive assumptions. The finite sample size behavior of the proposed test is studied by simulations and it is compared to that of a test based on the sample coefficient of variation.     

线性脉冲控制系统的能控性与最优控制

首先讨论了一类线性随机脉冲控制系统的精确能控性质,给出了该类控制系统的脉冲精确能控的等价的代数判据.然后提出了一个确定性的二维线性脉冲控制系统的时间-脉冲强度最优控制问题;利用动态规划原理,给出了脉冲最优控制的反馈形式和值函数的显式表达式;说明了值函数在整个平面上是连续的,在左右两个半平面的内部还是连续可微的.     

Admissible investment strategies in continuous trading

We consider a situation where relative prices of assets may change continuously and also have discrete jumps at random time points. The problem is the one of portfolio optimization. If the utility function used is the logarithm, we first argue that an optimal investment plan exists. Secondly, we show that any such plan has a certain optimality property known to hold also in discrete time models. Moreover, we show that this optimality criterion can be simplified significantly. In particular we show how admissibility can be related directly to observable characteristics of the investment strategy.