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.     

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.     

状态方程计算高分子共混物的比体积

基于一个简单的非均核链流体分子热力学模型,采用不同形式的微扰项,可构筑不同形式的高分子共混物系统的状态方程。方程已被应用于关联聚苯乙烯/聚2,6-二甲基苯醚(PS/PPO)、聚苯乙烯/聚乙烯甲醚(PS/PVME)、聚苯乙烯/聚丁二烯(PS/PBD)、聚醚砜/聚氧乙烯(PESP/PEO)等高分子共混物的比体积。结果显示,用一个与温度无关的二元相互作用可调参数可满意关联所选体系的比体积,并可预测所选体系的比体积。     

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.     

Solvability of perturbation solutions in DSGE models

We prove that the undetermined Taylor series coefficients of local approximations to the policy function of arbitrary order in a wide class of discrete time dynamic stochastic general equilibrium (DSGE) models are solvable by standard DSGE perturbation methods under regularity and saddle point stability assumptions on first order approximations. Extending the approach to nonstationary models, we provide necessary and sufficient conditions for solvability, as well as an example in the neoclassical growth model where solvability fails. Finally, we eliminate the assumption of solvability needed for the local existence theorem of perturbation solutions, complete the proof that the policy function is invariant to first order changes in risk, and attribute the loss of numerical accuracy in progressively higher order terms to the compounding of errors from the first order transition matrix.     

Board size,corporate regulations and firm valuation in an emerging market: a simultaneous equation approach

We investigate the association between board size and firm valuation for a sample of 169 firms from 2002 to 2011 in South Africa (SA). The SA corporate context is interestingly and uniquely characterised by an urgency to meet affirmative action regulations, such as black empowerment in board appointments, limited qualified and experienced directors, especially black directors, concentrated ownership, weak enforcement of corporate regulations and greater government ownership. These features make SA corporate boards perform a weaker agency (advisory, monitoring and disciplining) role than Western European and US boards, but a stronger resource dependence role, by providing access to resources, such as business contacts and contracts. This suggests that any positive impact of board size on firm valuation is likely to depend on the effective execution of the resource dependence role more than the agency role. Our results suggest that board size has a positive association with firm valuation, consistent with larger boards providing better access to resources. Overall, our results support the resource dependence role of boards more than their agency role. The results are robust across a raft of econometric models that control for different types of endogeneity, as well as different types of accounting and market-based firm valuation measures.     

Independence in bank governance structure: Empirical evidence of effects on bank risk and performance

We investigate how different governance arrangements affect risk and return in banks. Using a new data set for UK banks over the period 2003–2012, we employ a simultaneous equations framework to control for the reciprocal relationship between risk and return. We show that separation of the roles of CEO and Chairman increases bank risk without causing a concurrent increase in return. We also find that oversight by a Remuneration Committee and Non-Executive Directors (NEDs) lowers the probability of bank failure, indicating that empowering an independent Chairman has different effects from empowering independent NEDs. Overall, our results underline the importance of accounting for the heterogeneity in corporate governance arrangements within banks.     

Stability and determinacy conditions for mixed-type functional differential equations

This paper analyzes the solution of linear mixed-type functional differential equations with either predetermined or non-predetermined variables. Conditions characterizing the existence and uniqueness of a solution are given and related to the local stability and determinacy properties of the steady state. In particular, it is shown that the relationship between the uniqueness of the solution and the stability of the steady-state is more subtle than the one that holds for ordinary differential equations, and gives rise to new dynamic configurations.