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The expanded sovereign bond portfolios from the sizeable public interventions in the financial sector during the current crisis need close monitoring and analysis of emerging vulnerabilities. This chapter presents some conventional and new measures of market, credit, and liquidity risks for government bond portfolios, considered from the perspective of a sovereign debt manager. In particular, it examines duration, convexity, and VaR statistics as measures of market exposure; the contingent-claims approach as the most promising measure of credit risk exposure; and a VaR statistic as a measure of liquidity risk.

The purpose of this paper is to derive an easy‐to‐implement and highly accurate formula to approximate the change in the bond price resulting from a change in interest rates.

The bond price is raised to an infinitesimal power and the Taylor series expansion is applied. Then, using the well‐known modified duration and convexity, the new formula is obtained as a limiting case.

It is proved mathematically and illustrated by numerical examples that the new formula generates better results than both the traditional duration‐convexity and the exponential duration approximation formulas.

The new formula derived in this paper will be used by risk managers to perform stress‐testing on bond portfolios.

The purpose of this paper is to develop, extend and propose an improved proportional integral derivative (PID) rate control of a quadrotor unmanned aerial vehicle based on a convexity-based surrogated firefly algorithm.

An improved PID controller structure is proposed for the rate dynamics of the quadrotor. Optimality of the controller is ensured by a recent, simple yet efficient firefly optimization method. The hybrid structure is further enhanced with a convexity-based surrogated model function.

Monte Carlo, transient response, error metrics and histogram distribution analyzes are conducted to show the performance of the proposed controller. The performance of the proposed method is evaluated under various convex combination values to further investigate the effect of the proposed surrogated model. According to the results, the proposed method is capable of controlling the rate quadrotor dynamics with the steady-state error of 0.0023 (rad/s) for P, −0.0024 (rad/s) for Q and 0 (rad/s) for the R state, respectively. Also, the least mean objective value is achieved at = 0 value of convexity in Monte Carlo trials.

The originality of this paper is to propose an improved PID rate controller with a convexity-based surrogated firefly algorithm.

This is an attempt to better bridge the gap between the mathematical and the engineering/physical aspects of the topic. The authors trace the different sources of non-convexification in the context of topology optimization problems starting from domain discretization, passing through penalization for discreteness and effects of filtering methods, and end with a note on continuation methods.

Starting from the global optimum of the compliance minimization problem, the authors employ analytical tools to investigate how intermediate density penalization affects the convexity of the problem, the potential penalization-like effects of various filtering techniques, how continuation methods can be used to approach the global optimum and how the initial guess has some weight in determining the final optimum.

The non-convexification effects of the penalization of intermediate density elements simply overshadows any other type of non-convexification introduced into the problem, mainly due to its severity and locality. Continuation methods are strongly recommended to overcome the problem of local minima, albeit its step and convergence criteria are left to the user depending on the type of application.

In this article, the authors present a comprehensive treatment of the sources of non-convexity in density-based topology optimization problems, with a focus on linear elastic compliance minimization. The authors put special emphasis on the potential penalization-like effects of various filtering techniques through a detailed mathematical treatment.

Two anisotropic yield criteria, that employ quadratic stress functions and have been extensively used for the elastoplastic analysis of composite materials, are considered. Proposed by Hoffman and by Sun, both these criteria have been formulated using nine parameters. With appropriate choice of parameters they reduce to the well‐known isotropic von Mises criterion and the anisotropic Hill criterion. This paper investigates the convexity, which is an essential condition for any plasticity model, for these criteria in the principal stress space. In each case two orthogonal sections ‐ deviatoric and volumetric ‐ are used to study the shapes of the ensuing curves. Illustrative three‐dimensional plots are included. It is concluded that, while simple interrelationships between the parameters ensure convexity of the Hoffman criterion, conditions for the Sun criterion are quite stringent.

Interest rate risk hedge strategies usually assume that term structure of interest rates in moving under a specific way. If a real term structure is moving differently from the assumed term structure movement, the interest rate risk hedge strategies assuming the special term structure movement may incur unexpected large loss for a bond portfolio manager. Hence an interest rate risk hedge strategy which could be effective under various types of term structure movements has been strongly needed by bond portfolio managers. Duration vector strategies have been developed to satisfy this practical need. To allow various types of term structure movements, duration vector strategies assume multi-factor models for the term structure movement. When a duration vector strategy is considered as a generalization of a duration strategy which is a single factor model for the term structure movement, there will be a generalized concept which measures convexity of a bond under the duration vector model. This study identifies the convexity property of an option embedded bond portfolio under ‘key rate duration model‘ which is a kind of duration vector model suggested by Ho (1992).

Shaft orbit is an important characteristic for vibration monitoring and diagnosing system of hydroelectric generating set. Because of the low accuracy and poor reliability of traditional methods in identifying the shaft orbit moving direction (MD), the purpose of this paper is to present a novel automatic identification method based on trigonometric function and polygon vector (TFPV).

First, some points on shaft orbit were selected with inter‐period acquisition method and joined together orderly to form a complex plane polygon. Second, by using the coordinate transformation and rotation theory, TFPV were applied comprehensively to judge the concavity or convexity of the polygon vertices. Finally, the shaft orbit MD is identified.

The simulation and experiment demonstrate that the method proposed can effectively identify the common shaft orbit MD.

In order to identity the shaft orbit MD effectively, a novel automatic identification method based on TFPV is proposed in this paper. The problem of identifying the shaft orbit MD is transformed into the problem about orientation of complex polygons, which are formed orderly by points on orbit shaft, and TFPV are applied comprehensively to judge the concavity or convexity of the polygon vertices.

This paper proposes the use of a gauge function as a measure of technical efficiency. The measure of technical inefficiency from a gauge function is desirable as the estimation of a gauge function is not subject to the endogeneity problem under the behavioral assumption of profit maximization in the competitive market.

The authors address three important properties of a gauge function, i.e. linear homogeneity, monotonicity and convexity in inputs and outputs, and show how such properties are utilized in its estimation. Then, the authors apply the estimation of a gauge function to US Blacksmiths in 1850 and 1880 to show that a failure to satisfy such properties may lead to an incorrect inference on the technical efficiency.

The authors find that the Blacksmiths in the 1850s were technically more efficient than the ones in the 1880s, indicating technical regress in Blacksmithing when the properties are satisfied.

This paper introduces a measure of technical inefficiency from a gauge function and shows how to estimate the gauge function parametrically for the measure. The authors show McFadden's gauge function and its properties, which differ from the properties of other distance functions. The authors emphasize linear homogeneity as well as monotonicity and convexity in inputs and outputs, which must be satisfied in the estimation of a gauge function.

This paper aims to examine the conditional and nonlinear relationship between price-earnings (P/E) ratio and payout ratio. A common finding of previous studies using linear regression model is that the P/E ratio is positively related to the dividend payout ratio. However, none of them investigates the condition under which the positive relationship holds.

This paper uses the fixed effects model to investigate the conditional and nonlinear relationship between P/E ratio and payout ratio. With the inclusion of fundamental factors and investor sentiment, this model allows for nonlinear relationship to be conditioned on the return on equity and the required rate of return.

Based on the annual data of industries in the USA over the period of 1998-2014, this paper produces new evidence indicating that when the return on equity is greater (less) than the required rate of return, the P/E ratio and dividend payout ratio exhibit a negative (positive) relationship and positive (negative) convexity.

Due to the curvature relationship between P/E ratio and payout ratio, the corporate managers and stock investors should pay more attention to the reduction in payout ratio than the rising payout ratio and the companies with low payout ratios than the companies with high payout ratios.

No previous study has tackled the issue of conditional and nonlinear relationship between P/E ratio and payout ratio. This paper attempts to fill the gap by allowing for nonlinear relationship conditional on the relative values of the return on equity and the required rate of return.

The purpose of this paper is to gain a better understanding of the market timing skills displayed by hedge fund managers during the 2007‐08 financial crisis.

The performance of a market timer can be measured through the 1966 Treynor and Mazuy model, provided the regression alpha is properly adjusted by using the cost of an option‐based replicating portfolio, as shown by Hübner. The paper adapts this approach to the case of multi‐factor models with positive, negative or neutral betas. This new approach is applied on a sample of hedge funds whose managers are likely to exhibit market timing skills. This concentrates on funds that post weekly returns, and analyzes three hedge funds strategies in particular: long‐short equity, managed futures, and funds of hedge funds. The paper analyzes a particular period during which the managers of these funds are likely to magnify their presumed skills, namely around the financial and banking crisis of 2008.

Some funds adopt a positive convexity as a response to the US market index, while others have a concave sensitivity to the returns of an emerging market index. Thus, the paper identifies “positive”, “mixed” and “negative” market timers. A number of signs indicate that only positive market timers manage to acquire options below their cost, and deliver economic significant performance, even in the midst of the financial crisis. Negative market timers, by contrast, behave as if they were forced to sell options without getting the associated premium. This behaviour is interpreted as a possible result of re sales, leading them to liquidate positions under the pressure of redemption orders, and inducing negative performance adjusted for market timing.

The paper suggests that the convexity in returns that is generally associated with market timing can be attributed to three sources: timing skills, exposure to nonlinear risk factors, or liquidity pressures. It manages to identify the impact of the latter two effects in the context of hedge funds.