非线性延迟系统Runge-Kutta方法的稳定性探讨

针对时间依赖型的非线性多变延迟系统,采用变步长的Runge-Kutta方法求解,证明了匹配一定插值方法的代数稳定的Runge-Kutta方法是VR稳定的。     

Can good marketing carry a bad product? Evidence from the motion picture industry

We examine the relative roles of marketing actions and product quality in determining commercial success. Using the motion picture context, in which product quality is difficult for consumers to anticipate and information on product success is available for different points in time, we model the effects of studio actions and movie quality on a movie’s sales during different phases of its theatrical run. For a sample of 331 recent motion pictures, structural equation modeling demonstrates that studio actions primarily influence early box office results, whereas movie quality influences both short- and long-term theatrical outcomes. The core results are robust across moderating conditions. We identify two data segments with follow-up latent class regressions and explore the degree of studio actions needed to “save” movies of varying quality. We finally offer some implications for research and management.     

PROPERTIES OF OPTION PRICES IN MODELS WITH JUMPS

We study convexity and monotonicity properties of option prices in a model with jumps using the fact that these prices satisfy certain parabolic integro–differential equations. Conditions are provided under which preservation of convexity holds, i.e., under which the value, calculated under a chosen martingale measure, of an option with a convex contract function is convex as a function of the underlying stock price. The preservation of convexity is then used to derive monotonicity properties of the option value with respect to the different parameters of the model, such as the volatility, the jump size, and the jump intensity.     

The (un)importance of geographical mobility in the Great Recession

Unemployment during and after the Great Recession has been persistently high. One concern is that the housing bust reduced geographical mobility and prevented workers from moving for jobs. We characterize flows out of unemployment that are related to geographical mobility to construct an upper bound on the effect of mobility on unemployment between 2007 and 2012. The effect of geographical mobility is always small: Using pre-recession mobility rates, decreased mobility can account for only an 11 basis points increase in the unemployment rate over the period. Using dynamics of renter geographical mobility in this period to calculate homeowner counterfactual mobility, delivers similar results. Using the highest mobility rate observed in the data, reduced mobility accounts for only a 33 basis points increase in the unemployment rate.     

三种电离层射线追踪自导引算法比较

通过建立电离层模型和地磁场模型,采用龙格库塔法求解Haselgrove方程,得到相应的射线路径参数,实现了电离层三维射线追踪。针对射线追踪无法进行自导引计算,分别采用牛顿差分自导引算法、基于变分方程的牛顿法以及单纯形法实现了射线追踪的自导引,并给出了详细的算法分析。重点对变分方程及其二阶微分的求解进行了详细推导。最后对以上三种自导引算法进行性能比较,仿真结果表明:基于变分方程的自导引算法优于其他两种自导引算法。     

EXPLICIT SOLUTIONS OF CONSUMPTION-INVESTMENT PROBLEMS IN FINANCIAL MARKETS WITH REGIME SWITCHING

We consider a consumption and investment problem where the market presents different regimes. An investor taking decisions continuously in time selects a consumption–investment policy to maximize his expected total discounted utility of consumption. The market coefficients and the investor's utility of consumption are dependent on the regime of the financial market, which is modeled by an observable finite-state continuous-time Markov chain. We obtain explicit optimal consumption and investment policies for specific HARA utility functions. We show that the optimal policy depends on the regime. We also make an economic analysis of the solutions, and show that for every investor the optimal proportion to allocate in the risky asset is greater in a "bull market" than in a "bear market." This behavior is not affected by the investor's risk preferences. On the other hand, the optimal consumption to wealth ratio depends not only on the regime, but also on the investor's risk tolerance: high risk-averse investors will consume relatively more in a "bull market" than in a "bear market," and the opposite is true for low risk-averse investors.     

Modeling Clustered Ordered Categorical Data: A Survey

This article surveys various strategies for modeling ordered categorical (ordinal) response variables when the data have some type of clustering, extending a similar survey for binary data by Pendergast, Gange, Newton, Lindstrom, Palta & Fisher (1996). An important special case is when repeated measurement occurs at various occasions for each subject, such as in longitudinal studies. A much greater variety of models and fitting methods are available than when a similar survey for repeated ordinal response data was prepared a decade ago (Agresti, 1989). The primary emphasis of the review is on two classes of models, marginal models for which effects are averaged over all clusters at particular levels of predictors, and cluster-specific models for which effects apply at the cluster level. We present the two types of models in the ordinal context, review the literature for each, and discuss connections between them. Then, we summarize some alternative modeling approaches and ways of estimating parameters, including a Bayesian approach. We also discuss applications and areas likely to be popular for future research, such as ways of handling missing data and ways of modeling agreement and evaluating the accuracy of diagnostic tests. Finally, we review the current availability of software for using the methods discussed in this article.     

PRICING ASIAN OPTIONS FOR JUMP DIFFUSION

We construct a sequence of functions that uniformly converge (on compact sets) to the price of an Asian option, which is written on a stock whose dynamics follow a jump diffusion. The convergence is exponentially fast. We show that each element in this sequence is the unique classical solution of a parabolic partial differential equation (not an integro‐differential equation). As a result we obtain a fast numerical approximation scheme whose accuracy versus speed characteristics can be controlled. We analyze the performance of our numerical algorithm on several examples.     

Simultaneous Estimation of Legal and Illegal Supply and Demand: The Case of Motion Pictures

Prior research into illegal goods has typically looked at one-way effects, such as illegal demand on legal demand. This research investigates a previously unexamined component of the market, illegal supply. The authors examine the supply and demand of legal goods and their illegal counterparts as a market system of four interdependent components. This research makes theoretical and empirical contributions by evaluating illegal supply in this system. Simultaneous equations estimate each market component on the others using data from the motion picture industry. The results find illegal supply has no effect on legal supply (movie screens), positive effects on illegal demand (piracy downloads), and some effect on legal demand (box office revenues). Timing effects highlight this: illegal supply has a positive effect on legal demand during a film’s opening week, but no effect post-launch. The other market components have positive effects on illegal supply (except legal supply, which is negative in the opening week). Additionally, illegal demand has a negative effect on legal demand during the opening week of release, but not in the subsequent weeks. This finding alleviates prior research tension as to whether piracy helps or hurts legal sales, as omitting illegal supply could result in biased estimates.