Optimal nonmyopic gambling strategy for the generalized Kelly criterion

We consider the optimal wagers to be made by a gambler who starts with a given initial wealth. The gambler faces a sequence of two-outcome games, i.e., “win” vs. “lose,” and wishes to maximize the expected value of his terminal utility. It has been shown by Kelly, Bellman, and others that if the terminal utility is of the form log x, where x is the terminal wealth, then the optimal policy is myopic, i.e., the optimal wager is always to bet a constant fraction of the wealth provided that the probability of winning exceeds the probability of losing. In this paper we provide a critique of the simple logarithmic assumption for the utility of terminal wealth and solve the problem with a more general utility function. We show that in the general case, the optimal policy is not myopic, and we provide analytic expressions for optimal wager decisions in terms of the problem parameters. We also provide conditions under which the optimal policy reduces to the simple myopic case. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 639–654, 1997     

灰色层次分析法战术通信网抗干扰效能评估

构建了战术通信网抗干扰效能评估指标体系,运用灰色层次分析法和群组决策特征根算法对抗干扰效能进行了评估。评估结果表明,该抗干扰效能一般,需要采取相关抗干扰对策以提高其抗干扰能力。     

基于BP神经网络的雷达网抗干扰性能综合评估

在分析目前综合评估雷达网抗干扰性能时遇到困难后,探讨了利用BP人工神经网络良好的非线性函数逼近特性来解决这一问题的可行性,并分析了在用这种方法建模评估的过程中需要注意的各种问题;其中侧重对在具体构造评估模型时输入输出评估指标集的确定方法和模型的训练验证方法进行了研究,并进一步分析了建立的模型可能的用途。最后指出这种思路也可以推广到对类似的复杂信息系统的综合评估中。     

模糊Petri网在空舰导弹武器系统效能分析中的应用

空舰导弹武器系统综合效能分析不但对导弹的定型起着一定作用,而且对装载该导弹的作战飞机的作战效能都具有重要的意义。依据空舰导弹武器系统的战技指标要求,运用模糊Petri网的原理结合层次分析法,对导弹武器的性能采取定性分析与定量分析相结合,以定量分析为主的方法进行评价。仿真实例对某型空舰导弹系统效能进行评价,结果表明它是一种方便、实用、可行的方法。     

分布式A2C2决策队设计

现代战争的特点是高度的分布式协同作战。面对瞬息万变的战场需求 ,完成分布协同作战的指挥自动化系统 ,就必须能够自动适应战场需求变化 ,不断改变指挥系统组织结构。因此 ,实现指挥自动化系统的中心工作是建立 C2系统自适应变结构决策队组织。论述了建立自适应分布式指挥决策组织结构的有关问题 ,研究了在分布式条件下 ,自适应 C2决策队结构的设计。     

辅助鞅下投资消费资产模型的一些基本性质

针对所给出的有交易费的资产模型,引入了资产折算函数,并利用辅助鞅和凸函数对偶方法,讨论了该模型下折算资产优化的性质.     

A comparative study of three tool replacement/operation sequencing strategies in a flexible manufacturing system

This paper studies three tool replacement/operation sequencing strategies for a flexible manufacturing system over a finite time horizon: (1) failure replacement—replace the tool only upon failure, (2) optimal preventive tool replacement for a fixed sequence of operations, and (3) joint scheduling of the optimal preventive tool replacement times and the optimal sequence of operations. Stochastic dynamic decision models are used for strategies 2 and 3. The optimization criterion for strategies 2 and 3 is the minimization of the total expected cost over the finite time horizon. We will show through numerical studies that, with the same amount of information, the total expected costs can be reduced considerably by choosing an optimal strategy. Our conclusion is that in flexible manufacturing, optimal tool replacement and optimal operations sequencing are not separate issues. They should be considered jointly to minimize the expected total cost. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 479–499, 2000     

Distribution free bounds for service constrained (Q,r) inventory systems

A classical and important problem in stochastic inventory theory is to determine the order quantity (Q) and the reorder level (r) to minimize inventory holding and backorder costs subject to a service constraint that the fill rate, i.e., the fraction of demand satisfied by inventory in stock, is at least equal to a desired value. This problem is often hard to solve because the fill rate constraint is not convex in (Q, r) unless additional assumptions are made about the distribution of demand during the lead‐time. As a consequence, there are no known algorithms, other than exhaustive search, that are available for solving this problem in its full generality. Our paper derives the first known bounds to the fill‐rate constrained (Q, r) inventory problem. We derive upper and lower bounds for the optimal values of the order quantity and the reorder level for this problem that are independent of the distribution of demand during the lead time and its variance. We show that the classical economic order quantity is a lower bound on the optimal ordering quantity. We present an efficient solution procedure that exploits these bounds and has a guaranteed bound on the error. When the Lagrangian of the fill rate constraint is convex or when the fill rate constraint does not exist, our bounds can be used to enhance the efficiency of existing algorithms. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 635–656, 2000     

Solving partially observable agent‐intruder games with an application to border security problems

In this paper, we introduce partially observable agent‐intruder games (POAIGs). These games model dynamic search games on graphs between security forces (an agent) and an intruder given possible (border) entry points and high value assets that require protection. The agent faces situations with dynamically changing, partially observable information about the state of the intruder and vice versa. The agent may place sensors at selected locations, while the intruder may recruit partners to observe the agent's movement. We formulate the problem as a two‐person zero‐sum game, and develop efficient algorithms to compute each player's optimal strategy. The solution to the game will help the agent choose sensor locations and design patrol routes that can handle imperfect information. First, we prove the existence of ?‐optimal strategies for POAIGs with an infinite time horizon. Second, we introduce a Bayesian approximation algorithm to identify these ?‐optimal strategies using belief functions that incorporate the imperfect information that becomes available during the game. For the solutions of large POAIGs with a finite time horizon, we use a solution method common to extensive form games, namely, the sequence form representation. To illustrate the POAIGs, we present several examples and numerical results.     

基于微惯导随机误差时间序列建模的改进组合导航方法

针对低精度、低成本微机电惯性测量单元随机误差建模效果不理想会极大影响组合导航性能的难题,采用时间序列分析方法建立了微机电惯性测量单元随机误差的自回归滑动平均模型,通过对卡尔曼滤波器的状态变量进行增广,建立系统动力学方程和观测方程,实现对零偏误差的在线估计。实测数据分析验证了该随机误差建模的有效性。实测数据处理结果表明,该方法能够显著提高低成本微惯性解算外推精度,增强微惯性/卫星组合导航可靠性。