First passage game

Appealing to the theory of stochastic games, a two-person, zero-sum first passage game, which may be viewed as a generalization of the first passage decision problem, is developed. In the first passage game, the players have stationary optional strategies and the values are unique and these can be computed using an algorithm for terminating stochastic games. It is also shown that the solution of a recurrence game is closely related to that of the first passage game. Finally, it is shown that a finite step stochastic game with nonstationary transition probabilities and payoffs can be converted to a first passage game whose solution yields a solution of the original finite step game. The first passage game so obtained has stationary transition probabilities and payoffs. Because of its special structure, the solution method reduces to a dynamic programming recursion in the context of games.     

A lower bound for the transition density function of a stochastic differential equation

Let W_t be a one-dimensional Brownian motion on the probability space (Ω,F,P), and let dx_t = a(x_t)dt + b(x_t)dw_t, b²(x) > 0, be a one-dimensional Ito stochastic differential equation. For a(x) = a₀ + a₁x + … + a_nxⁿ on a bounded interval we obtain a lower bound for p(t,x,y), the transition density function of the homogeneous Markov process x_t, depending directly on the coefficients a₀,a₁, …, a_n, and b(x).     

A stochastic Newton-Raphson method

A stochastic approximation procedure of the Robbins-Monro type is considered. The original idea behind the Newton-Raphson method is used as follows. Given n approximations X₁,…, X_n with observations Y₁,…, Y_n, a least squares line is fitted to the points (X_m, Y_m),…, (X_n, Y_n) where m<n may depend on n. The (n+1)st approximation is taken to be the intersection of the least squares line with y=0. A variation of the resulting process is studied. It is shown that this process yields a strongly consistent sequence of estimates which is asymptotically normal with minimal asymptotic variance.     

A STOCHASTIC LOGISTIC MODEL WITH TIME DELAY

The stochastic version of the logistic model for population growth is generalized to take account of continuously distributed time delay with an exponentially decaying kernel. The theory of diffusion processes is used to analyse the probability density function of the population size. The explicit expression for the stationary distribution is worked out and the effect of time delay on various statistics is discussed.     

Geostochastic calculus

A stochastic calculus for a family of continuous measure-valued Markov processes is developed. Such processes arise naturally in the construction of stochastic models of spatially distributed populations. The stochastic calculus is a tool whereby a class of density-dependent models can be studied in terms of the multiplicative measure diffusion process. In this paper the stochastic integral is introduced in the space-time setting and a Cameron-Martin-Girsanov theorem is established.     

A Bayesian approach to statistical inference in stochastic DEA

Stochastic DEA can deal effectively with noise in the non-parametric measurement of efficiency but unfortunately formal statistical inference on efficiency measures in not possible. In this paper, we provide a Bayesian approach to the problem organized around simulation techniques that allow for finite-sample inferences on efficiency scores. The new methods are applied to efficiency analysis of the Greek banking system for the period 1993–1999. The results show that the majority of the Greek banks operate close to best market practices.     

Sequential and Simultaneous Decision Making for Optimizing Health Care Resource Flexibilities

Health care administrators commonly employ two types of resource flexibilities (demand upgrades and staffing flexibility) to efficiently coordinate two critical internal resources, nursing staff and beds, and an external resource (contract nurses) to satisfy stochastic patient demand. Under demand upgrades, when beds are unavailable for patients in a less acute unit, patients are upgraded to a more acute unit if space is available in that unit. Under staffing flexibility, nurses cross‐trained to work in more than one unit are used in addition to dedicated and contract nurses. Resource decisions (beds and staffing) can be made at a single point in time (simultaneous decision making) or at different points in time (sequential decision making). In this article, we address the following questions: for each flexibility configuration, under sequential and simultaneous decision making, what is the optimal resource level required to meet stochastic demand at minimum cost? Is one type of flexibility (e.g., demand upgrades) better than the other type of flexibility (e.g., staffing flexibility)? We use two‐stage stochastic programming to find optimal resource levels for two nonhomogeneous hospital units that face stochastic demand following a continuous, general distribution. We conduct a full‐factorial numerical experiment and find that the benefit of using staffing flexibility on average is greater than the benefit of using demand upgrades. However, the two types of flexibilities have a positive interaction effect and they complement each other. The type of flexibility and decision timing has an independent effect on system performance (capacity and staffing costs). The benefits of cross‐training can be largely realized even if beds and staffing levels have been determined prior to the establishment of a cross‐training initiative.     

幼儿园开展游戏分享环节的现状及启示——基于江苏省幼儿园的调查

笔者通过问卷法、访谈法和观察法的综合运用,对江苏省的318名幼儿园教师进行了问卷调研,并选取N市某公立园的3个班级和6位教师作为观察和访谈对象。研究结果表明,在时间安排上,分享环节并非每次游戏后都会开展,不同年龄班的分享时长存在一定差异;在分享内容上,话题主要围绕角色游戏、结构游戏和美工游戏开展,更多涉及幼儿的社会领域发展经验,经常分享游戏中遇到的困难及解决策略;在开展形式上,不同年龄班游戏话题的开启方式各异,分享方法丰富多样,分享地点呈现多样化,但目前仍以全班讨论形式为主。据此,笔者从教师、园所和社会三个层面,提出了优化游戏分享环节开展现状的具体建议。     

借贷能力、风险收益与新型农业经营主体经营效率

通过构建一个新型农业经营主体与金融组织讨价还价的理论模型,在纳什议价均衡的基础上分析新型经营主体最优产出水平与其借贷能力、风险收益的关系。基于中国12省的微观调查数据,采用双边随机边界检验,对理论模型进行了实证研究,结果表明：借贷能力不足是新型经营主体经营无效率的主导因素,最终使平均净效率下降了8.13%;正规金融机构和民间借贷均对新型经营主体的经营效率有显著影响,并且民间借贷对经营效率的影响更强;新型经营主体的负责人能力、盈利能力、组织化程度等,与其经营效率呈正相关关系。提出应通过金融体系创新、完善民间借贷法规等途径,降低新型农业经营主体的融资约束,提高其负责人的经营水平,加强新型经营主体的组织化程度。     

The Beta Product Distribution with Complex Parameters

The family consisting of the distributions of products of two independent beta variables is extended to include cases where some of the parameters are not positive but negative or complex. This “beta product” distribution is expressible as a Meijer G function. An example (from risk theory) where such a distribution arises is given: an infinite sum of products of independent random variables is shown to have a distribution that is the product convolution of a complex-parameter beta product and an independent exponential. The distribution of the infinite sum is a new explicit solution of the stochastic equation X = (in law) B(X + C). Characterizations of some G distributions are also proved.