Adaptive synchronization of identical chaotic and hyper-chaotic systems with uncertain parameters

This paper addresses a unified mathematical expression describing a class of chaotic systems, for which the problem of adaptive synchronization between two nearly identical chaotic and hyper-chaotic systems with uncertain parameters is studied. Based on Lyapunov stability theory, a novel adaptive synchronization controller is designed, and the analytic expression of the controller and the adaptive laws of parameters are developed. The controller is simple and systemic, no parameters of the slave system are included in the controller, and, for some specific error systems, the controller can be simplified ulteriorly. New chaotic and a new hyper-chaotic systems with uncertain parameters are taken as the examples to show the effectiveness of the proposed adaptive synchronization method.     

Empirical study of the scaling behavior of the amplitude–frequency distribution of the Hilbert–Huang transform and its application in sunspot time series analysis

Investigating long-range correlation by the Hurst exponent, H$H$, is crucial in the study of time series. Recently, empirical-mode-decomposition-based arbitrary-order Hilbert spectral analysis (EMD-HSA) has been proposed to numerically obtain without proof a scaling relationship, generated from the amplitude–frequency distribution, related to H$H$. We propose a formalism to empirically study EMD-HSA, to deduce its scaling exponent ξ(q)$\xi \left(q\right)$ from the perspective of EMD-based arbitrary-order Hilbert marginal spectrum (EMD-HMS), and to numerically compare the results with the expected H$H$. EMD-HSA and EMD-HMS experiments show that, by incompletely removing (quasi-)periodic trends, the sunspot series should have an H$H$ value around 0.12.     

Implied Volatility of Leveraged ETF Options

Abstract

This paper studies the problem of understanding implied volatilities from options written on leveraged exchanged-traded funds (LETFs), with an emphasis on the relations between LETF options with different leverage ratios. We first examine from empirical data the implied volatility skews for LETF options based on the S&P 500. In order to enhance their comparison with non-leveraged ETFs, we introduce the concept of moneyness scaling and provide a new formula that links option implied volatilities between leveraged and unleveraged ETFs. Under a multiscale stochastic volatility framework, we apply asymptotic techniques to derive an approximation for both the LETF option price and implied volatility. The approximation formula reflects the role of the leverage ratio, and thus allows us to link implied volatilities of options on an ETF and its leveraged counterparts. We apply our result to quantify matches and mismatches in the level and slope of the implied volatility skews for various LETF options using data from the underlying ETF option prices. This reveals some apparent biases in the leverage implied by the market prices of different products, long and short with leverage ratios two times and three times.     

Game Options Analysis of the Information Role of Call Policies in Convertible Bonds

Abstract

In debt financing, existence of information asymmetry on the firm quality between the firm management and bond investors may lead to significant adverse selection costs. We develop the two-stage sequential dynamic two-person game option models to analyse the market signalling role of the callable feature in convertible bonds. We show that firms with positive private information on earning potential may signal their type to investors via the callable feature in a convertible bond. We present the variational inequalities formulation with respect to various equilibrium strategies in the two-person game option models via characterization of the optimal stopping rules adopted by the bond issuer and bondholders. The bondholders’ belief system on the firm quality may be revealed with the passage of time when the issuer follows his optimal strategy of declaring call or bankruptcy. Under separating equilibrium, the quality status of the firm is revealed so the information asymmetry game becomes a new game under complete information. To analyse pooling equilibrium, the corresponding incentive compatibility constraint is derived. We manage to deduce the sufficient conditions for the existence of signalling equilibrium of our game option model under information asymmetry. We analyse how the callable feature may lower the adverse selection costs in convertible bond financing. We show how a low-quality firm may benefit from information asymmetry and vice versa, underpricing of the value of debt issued by a high-quality firm.     

Construction of blow-up sequences for the prescribed scalar curvature equation on S n . II. Annular domains

Using the Lyapunov–Schmidt reduction method, we describe how to use annular domains to construct (scalar curvature) functions on S ⁿ (n ≥ 6), so that each one of them enables the conformal scalar curvature equation to have a blowing-up sequence of positive solutions. The prescribed scalar curvature function is shown to have C ^{n - 1, β} smoothness.     

Apparent anomalous fading of thermoluminescence associated with competition with radiationless transitions

Anomalous fading of thermoluminescence (TL) is the effect of a fading which is significantly faster than what is warranted by the trapping parameters which are evaluated from the features of the TL peak in question. A previous work suggested that in certain cases, apparent anomalous fading may be a normal fading in disguise. The idea was that, at least in some cases, radiationless transitions into competing recombination centers may yield a very narrow peak which, while using either the curve fit technique or the different peak shape method will result in very high values of effective activation energy E and frequency factor s which, in turn, will yield an apparent life-time orders of magnitude higher than the real one. The question has been raised whether this anomaly is observable only when the peak shape methods are utilized and in particular, can the same effect occur when the broadly used initial-rise method is applied. It is demonstrated in this work that under similar circumstances of competition, very high effective values of E and s are evaluated which result in very high life-times when the activation energy is evaluated by the initial-rise method. Thus, the explanation of apparent anomalous fading as being a normal decay in disguise, is extended to cases in which the initial-rise method is utilized for the parameter evaluation.     

Distinguishing between the interior pressures induced from two independent sources within a room using the probabilistic approach

In this paper, a probabilistic approach is introduced and used to distinguish between the interior pressures that are induced from two independent sound sources within a rectangular room. One source is a vibrating wall of the room and the other is an interior point source. The model is set up using the modal analysis method. In the probabilistic method, the probability densities of the uncertain acoustic model parameters are computed. The values of highest probability density are identified and assigned to the uncertain parameters in the acoustic model. The contributions of the sound sources to the total pressure are then obtained from the acoustic model input with the identified parameters. The effects of the modal truncations, the modeling errors, and the measurement locations on the accuracies of the identification process are studied.     

On closedness of convex sets in Banach lattices

Positivity - Let X be a Banach lattice. A well-known problem arising from the theory of risk measures asks when order closedness of a convex set in X implies closedness with respect to the topology...