A note on the existence of unique equivalent martingale measures in a Markovian setting

Simple sufficient conditions for the existence of a unique equivalent martingale measure are provided. Furthermore, these conditions give us a handle on situations where an equivalent martingale measure cannot exist. The existence of a unique equivalent martingale measure is of relevance to problems in mathematical finance. Two examples of models for which the question of existence was unresolved are studied. By means of our results existence of a unique equivalent measure up to an explosion time is proved.     

Asymptotically optimal estimation of smooth functionals for interval censoring, part 1

Estimation in the interval censoring model is considered. A class of smooth functionals is introduced, of which the mean is an example. The asymptotic information lower bound for such functionals can be represented as an inner product of two functions. In case 1, i.e. one observation time per unobservable event time, both functions can be given explicitly. We mainly consider case 2, with two observation times for each unobservable event time, in the situation that the observation times can not become arbitrarily close to each other. For case 2, one of the functions in the inner product can only be given implicitly as solution to a Fredholm integral equation. We study properties of this solution and, in a sequel to this paper, prove that the nonparametric maximum likelihood estimator of the functional asymptotically reaches the information lower bound.     

Effect of credible quality investment with Bertrand and Cournot competition

We show how credible revelation and ability to commit to quality choice effect equilibrium qualities and welfare when product market is either Bertrand or Cournot competition. We show that results depend on the type of competition but not generally on the cost of quality function. We show that with Bertrand competition, the equilibrium qualities are lower with credible commitment. Competition is moderated and producer surplus is higher and consumer surplus lower. With Cournot competition, higher quality will be better but lower quality will be worse with credible commitment. Consumer surplus is always greater with credible commitment and if cost does not increase too quickly with quality, producer surplus will also increase. Thus credible commitment is a collusive device with Bertrand competition but it can improve social welfare with Cournot competition. Received: February 8, 2000; revised version: February 14, 2002 RID="*" ID="*" The idea of this paper originated in the weekly workshops of Mordecai Kurz at Stanford. I am forever in debted to Mordecai and fellow students – Luis Cabral, Peter DeMarzo, John Hillas, Michihiro Kandori, Steve Langois, Patrick McAllister, Steve Sharpe, Peter Streufert, Steve Turnbull and Gyu-Ho Wang – for their criticism and encouragement. I also benefited from comments from Yi-Heng Chen, Jin-Li Hu, Kala Krishna, Jinji Naoto, Thomas J. Prusa, and Shyh-Fang Ueng at various later stages of this work. Last but not least, I am grateful for the detailed comments of the referee.     

A substitution orbit model of competitive innovations

Successful innovation and diffusion of technology can be attributed to the identification of the orbit of emerging new technologies that complement or substitute for existing technologies. This dynamism resembles the co-evolution process in an ecosystem. In an ecosystem, in order to maintain sustainable development, the complex interplay between competition and cooperation, typically observed in predator-prey systems, create a sophisticated balance. Given that an ecosystem can be used as a masterpiece system, this sophisticated balance can provide suggestive ideas for identifying an optimal orbit of competitive innovations with complement or substitution dynamism.Prompted by such a sophisticated balance in an ecosystem, this paper analyzes the optimal orbit of competitive innovations and, on the basis of an application of Lotka-Volterra equations, it reviews substitution orbits of Japan's monochrome to color TV system, fixed telephones to cellular telephones, cellular telephones to mobile Internet access service, and analog to digital TV broadcasting. On the basis of substitution orbits analyses, it attempts to extract suggestions supportive to identifying an optimal policy option in a complex orbit leading to expected orbit.Key findings include policy options that are effective in controlling parameters for Lotka-Volterra equations leading to expected orbit.     

Capital buffer and credit‐risk adjustments in Islamic and conventional banks

The main purpose of this article is to empirically investigate the interactions between changes in capital buffer and changes in credit risk, using panel data of Islamic and conventional banks located in the Middle East and North Africa (MENA) region over the period 1999–2016. A negative two‐way relationship between the changes in capital buffer and the changes in credit risk is found for the two types of banks, that is, banks tend to decrease their capital buffers in response to an increase in risk exposure and limit their risky activities in response to an increase in their capital buffers. Dividing our period of study into three subperiods to assess the effect of the last financial crisis 2007–08 on the adjustment process, we point out the negative bidirectional relationship between the changes in capital buffer and the changes in credit risk of the two types of banks is present for the three subperiods except the case of conventional banks during the precrisis period. Moreover, we provide evidence that Islamic banks adjust their capital buffer in response to the changes in credit risk regardless of the existence or not of a deposit insurance scheme. In contrast, the negative two‐way relationship between the changes in capital buffer and the changes in credit risk in conventional banks is found only in countries without deposit insurance schemes.     

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.     

PARTIAL HEDGING IN A STOCHASTIC VOLATILITY ENVIRONMENT

We consider the problem of partial hedging of derivative risk in a stochastic volatility environment. It is related to state-dependent utility maximization problems in classical economics. We derive the dual problem from the Legendre transform of the associated Bellman equation and interpret the optimal strategy as the perfect hedging strategy for a modified claim. Under the assumption that volatility is fast mean-reverting and using a singular perturbation analysis, we derive approximate value functions and strategies that are easy to implement and study. The analysis identifies the usual mean historical volatility and the harmonically averaged long-run volatility as important statistics for such optimization problems without further specification of a stochastic volatility model. The approximation can be improved by specifying a model and can be calibrated for the leverage effect from the implied volatility skew. We study the effectiveness of these strategies using simulated stock paths.     

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.     

基于螺旋谐振环结构的UWB同步开关噪声抑制电源平面

针对目前印制电路板中采用的同步开关噪声抑制方法抑制带宽较窄、全向性较差、电源平面有效使用面积小、结构复杂及对信号质量影响大的问题,提出了一种基于螺旋谐振环结构的超宽带同步开关噪声抑制平面,具有结构简单、阻带宽、抑制方向具有全向性、无需周期性电磁带隙结构的特点。通过研究其等效电路模型,使用三维有限元法（FEM）对所设计的结构提取了S参数,并进行了频域与时域分析与仿真。仿真结果表明：所提出的结构其同步开关噪声抑制深度在-40 dB时,阻带范围为0.13~20 GHz,抑制带宽达到19.87 GHz,有效降低了带隙中心频率;当注入噪声电压为1 V时,可将噪声电压抑制到0.25 mV;对比UC-EBG和Planar EBG结构,在-40 dB抑制深度时,抑制带宽分别提高了16.97 GHz和17.73 GHz。