On dividends in the phase–type dual risk model

The dual risk model assumes that the surplus of a company decreases at a constant rate over time, and grows by means of upward jumps which occur at random times with random sizes. In the present work, we study the dual risk renewal model when the waiting times are phase-type distributed. Using the roots of the fundamental and the generalized Lundberg’s equations, we get expressions for the ruin probability and the Laplace transform of the time of ruin for an arbitrary single gain distribution. Then, we address the calculation of expected discounted future dividends particularly when the individual common gains follow a phase-type distribution. We further show that the optimal dividend barrier does not depend on the initial reserve. As far as the roots of the Lundberg equations and the time of ruin are concerned, we address the existing formulae in the corresponding Sparre-Andersen insurance risk model for the first hitting time, and we generalize them to cover also the situations where we have multiple roots. We do that working a new approach and technique, approach we also use for working the dividends, unlike others, it can be also applied for every situation.     

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.     

The role of banks in the governance of nonfinancial firms: Evidence from Europe

The aim of our research is to investigate the important role of banks in the governance of companies listed in the Euronext 100 index. Primarily, this research seeks to examine the impact of a bank’s presence within a firm, as a creditor or shareholder, on firm performance, as well as the motivations of banks to acquire holdings, and whether the presence of a bank as a shareholder of a firm facilitates its access to bank loans. Empirical analyses are conducted with a sample of 86 nonfinancial institutions listed in the Euronext 100 index over the period 2008–2013 using the three-stage least squares method. The study shows, first, that the presence of a bank within a firm, as a creditor or shareholder, is positively related to firm performance. Moreover, the firm’s performance is an important determinant of the presence of bank shareholding. Finally, the presence of a bank as a shareholder of a firm does not facilitate its access to bank loans.     

Production planning and inventories optimization: A backward approach in the convex storage cost case

We study the deterministic optimization problem of a profit-maximizing firm which plans its sales/production schedule. The firm controls both its production and sales rates and knows the revenue associated to a given level of sales, as well as its production and storage costs. The revenue and the production cost are assumed to be respectively concave and convex. In Chazal et al. [Chazal, M., Jouini, E., Tahraoui, R., 2003. Production planning and inventories optimization with a general storage cost function. Nonlinear Analysis 54, 1365–1395], we provide an existence result and derive some necessary conditions of optimality. Here, we further assume that the storage cost is convex. This allows us to relate the optimal planning problem to the study of a backward integro-differential equation, from which we obtain an explicit construction of the optimal plan.     

线性代数教学实践中的体会

结合线性代数课程本身的特点和学生实际情况,通过对线性代数课程的教学实践,提出了线性代数抽象概念讲解要与具体实例相结合,激发学生的学习兴趣,提高学生分析、归纳、总结和演绎的基本素质,改进教学方法和手段等措施来提高课程的教学质量。     

A new higher-order weak approximation scheme for stochastic differential equations and the Runge–Kutta method

The authors report on the construction of a new algorithm for the weak approximation of stochastic differential equations. In this algorithm, an ODE-valued random variable whose average approximates the solution of the given stochastic differential equation is constructed by using the notion of free Lie algebras. It is proved that the classical Runge–Kutta method for ODEs is directly applicable to the ODE drawn from the random variable. In a numerical experiment, this is applied to the problem of pricing Asian options under the Heston stochastic volatility model. Compared with some other methods, this algorithm is significantly faster. This research was partly supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (C), 15540110, 2003 and 18540113, 2006, the 21st century COE program at Graduate School of Mathematical Sciences, the University of Tokyo, and JSPS Core-to-Core Program 18005.     

Bartlett adjustments for systems of linear equations with linear restrictions

Simple matrix formulae are derived for calculating a Bartlett adjustment to the likelihood ratio test statistic for testing linear parameter restrictions in a system of linear equations. For the special case of column and/or row restrictions on the matrix of coefficients the adjustment is a simple function of matrix dimensions being invariant to sample observations and the error covariance matrix. An example of testing for homogeneity and symmetry in a demand system is given.     

The geography of trade in goods and asset holdings

Gravity models have been widely used to describe bilateral trade in goods. Portes and Rey [Portes, R., Rey, H., 2005. The Determinants of Cross-Border Equity Flows. Journal of International Economics, 65(2), 269-296.] applied this framework to cross-border equity flows and found that distance, which proxies information asymmetries, is a surprisingly very large barrier to cross-border asset trade. We adopt a different point of view and explore the complementarity between bilateral trade in goods and bilateral asset holdings in a simultaneous gravity equations framework. Providing different instruments for both endogenous variables, we show that a 10% increase in bilateral trade raises bilateral asset holdings by 6% to 7%. The reverse causality is also significant, albeit smaller. Controlling for trade, the impact of distance on asset holdings is drastically reduced.     

Poisson Regression for Clustered Data

We compare five methods for parameter estimation of a Poisson regression model for clustered data: (1) ordinary (naive) Poisson regression (OP), which ignores intracluster correlation, (2) Poisson regression with fixed cluster‐specific intercepts (FI), (3) a generalized estimating equations (GEE) approach with an equi‐correlation matrix, (4) an exact generalized estimating equations (EGEE) approach with an exact covariance matrix, and (5) maximum likelihood (ML). Special attention is given to the simplest case of the Poisson regression with a cluster‐specific intercept random when the asymptotic covariance matrix is obtained in closed form. We prove that methods 1–5, except GEE, produce the same estimates of slope coefficients for balanced data (an equal number of observations in each cluster and the same vectors of covariates). All five methods lead to consistent estimates of slopes but have different efficiency for unbalanced data design. It is shown that the FI approach can be derived as a limiting case of maximum likelihood when the cluster variance increases to infinity. Exact asymptotic covariance matrices are derived for each method. In terms of asymptotic efficiency, the methods split into two groups: OP & GEE and EGEE & FI & ML. Thus, contrary to the existing practice, there is no advantage in using GEE because it is substantially outperformed by EGEE and FI. In particular, EGEE does not require integration and is easy to compute with the asymptotic variances of the slope estimates close to those of the ML.     

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.