On Modeling Questions In Security Valuation

After mentioning some deficiencies of the standard Black-Scholes model for the valuation of call options, we discuss discrete models which allow price changes of the underlying security at discrete time points only. It is shown that, given any distribution with a moment higher than 2, the paths of the Black-Scholes stock price process can be approximated uniformly as closely as one wishes by discrete paths generated by this distribution. Based on this approximation, discrete-time trading strategies are defined. Convergence (in measure and almost surely) of the corresponding financial gain processes is obtained. the results show the robustness of the Black-Scholes model.     

The Berry-esséen theorem for the subject-years method in mortality analysis with censored data

The test for the hypothesis that the mortality in the observed group is the same as that of a reference group by subject-years method is considered in this paper. We prove a Berry-Esséen type theorem for the test statistics studied in Berry (1983), which gives an upper bound for the convergence rates of test statistics to their limiting distributions.     

Hedging and Portfolio Optimization in Financial Markets with a Large Trader

We introduce a general continuous-time model for an illiquid financial market where the trades of a single large investor can move market prices. The model is specified in terms of parameter-dependent semimartingales, and its mathematical analysis relies on the nonlinear integration theory of such semimartingale families. The Itô–Wentzell formula is used to prove absence of arbitrage for the large investor, and, using approximation results for stochastic integrals, we characterize the set of approximately attainable claims. We furthermore show how to compute superreplication prices and discuss the large investor's utility maximization problem.     

Transient and asymptotic dynamics of reinforcement learning in games

Reinforcement learners tend to repeat actions that led to satisfactory outcomes in the past, and avoid choices that resulted in unsatisfactory experiences. This behavior is one of the most widespread adaptation mechanisms in nature. In this paper we fully characterize the dynamics of one of the best known stochastic models of reinforcement learning [Bush, R., Mosteller, F., 1955. Stochastic Models of Learning. Wiley & Sons, New York] for 2-player 2-strategy games. We also provide some extensions for more general games and for a wider class of learning algorithms. Specifically, it is shown that the transient dynamics of Bush and Mosteller's model can be substantially different from its asymptotic behavior. It is also demonstrated that in general—and in sharp contrast to other reinforcement learning models in the literature—the asymptotic dynamics of Bush and Mosteller's model cannot be approximated using the continuous time limit version of its expected motion.     

Linear-quadratic approximation, external habit and targeting rules

We examine the linear-quadratic approximation of nonlinear dynamic stochastic optimization problems. A discrete-time version of Magill [1977a. A local analysis of N-sector capital accumulation under uncertainty. Journal of Economic Theory 15(2), 211–219] is generalized to models with forward-looking variables paying special attention to second-order conditions. This is the ‘large distortions’ case in the literature. We apply the approach to monetary policy in a DSGE model with external habit in consumption. We then develop a condition for ‘target-implementability’, a concept related to ‘targeting rules’. Finally, we extend the approach to a comparison between cooperative and non-cooperative equilibria in a two-country model and show that the ‘small distortions’ approximation is inappropriate for this exercise.     

两级供应链分销模型的研究

本文探讨了最具代表性的两级供应链的分销模型,在前人研究的基础上通过构建与求解连续近似模型,得出分销中心的数目及其服务区域的面积,并通过模型的解来分析整个系统的成本结构。算例表明,模型的求解结果与事实相符,且将订货费同建设费、运营费、运输费一同考虑更能精确描述系统的成本结构。     

一种利用多核解卷积提高雷达角分辨力的方法

解卷积方法可以提高雷达的角分辨力,但传统的解卷积算法对噪声很敏感,且有可能无解。给出了多核解卷积方法的最优滤波器,分析了多核解卷积的输出信噪比,指出其抗噪声性能要优于单核解卷积。最后将多核解卷积的方法运用到单脉冲雷达中。仿真结果表明,在输入信噪比为20dB的情况下,该方法还能够得到很好的结果。     

Prior‐free Bayes Factors Based on Data Splitting

Bayes factors that do not require prior distributions are proposed for testing one parametric model versus another. These Bayes factors are relatively simple to compute, relying only on maximum likelihood estimates, and are Bayes consistent at an exponential rate for nested models even when the smaller model is true. These desirable properties derive from the use of data splitting. Large sample properties, including consistency, of the Bayes factors are derived, and a simulation study explores practical concerns. The methodology is illustrated with civil engineering data involving compressive strength of concrete.