On the L

A nonlinear generalized Degasperis-Procesi equation is investigated. Assuming that the strong solution of the equation is bounded in the sense of L∞R-norm and the initial data belong to the space L1(R)∩L2(R), we prove that the solutions are stable in the space L1(R)

Stability to a Generalized Degasperis-Procesi Equation

A nonlinear generalized Degasperis-Procesi equation is investigated. Assuming that the strong solution of the equation is bounded in the sense of L ∞ (R)-norm and the initial data belong to the space L 1 (R) ∩ L 2 (R), we prove that the solutions are stable in the space L 1 (R)

Optimal Asset Allocation for CRRA and CARA Insurers under the Vasicek Interest Rate Model

This paper considers the reinsurance-investment problem with interest rate risks under constant relative risk aversion and constant absolute risk aversion preferences, respectively. Stochastic control theory and dynamic programming principle are applied to investigate the optimal proportional reinsurance-investment strategy for an insurer under the Vasicek stochastic interest rate model. Solving the corresponding Hamilton-Jacobi-Bellman equation via the Legendre transform approach, the optimal premium allocation strategies maximizing the expected utilities of terminal wealth are derived. In addition, several sensitivity analyses and numerical illustrations are given to analyze the impacts of different risk preferences and interest rate fluctuation on the optimal strategies. We find that the asset allocation and reinsurance ratio of the insurer are correlated with risk preference coefficient and interest rate fluctuation, and the insurance company may adjust the reinsurance-investment strategy to deal with interest rate risk

Optimal Reinsurance-Investment Problem for an Insurer and a Reinsurer with Jump-Diffusion Process

The optimal reinsurance-investment strategies considering the interests of both the insurer and reinsurer are investigated. The surplus process is assumed to follow a jump-diffusion process and the insurer is permitted to purchase proportional reinsurance from the reinsurer. Applying dynamic programming approach and dual theory, the corresponding Hamilton-Jacobi-Bellman equations are derived and the optimal strategies for exponential utility function are obtained. In addition, several sensitivity analyses and numerical illustrations in the case with exponential claiming distributions are presented to analyze the effects of parameters about the optimal strategies

An Interval of No-Arbitrage Prices in Financial Markets with Volatility Uncertainty

In financial markets with volatility uncertainty, we assume that their risks are caused by uncertain volatilities and their assets are effectively allocated in the risk-free asset and a risky stock, whose price process is supposed to follow a geometric G-Brownian motion rather than a classical Brownian motion. The concept of arbitrage is used to deal with this complex situation and we consider stock price dynamics with no-arbitrage opportunities. For general European contingent claims, we deduce the interval of no-arbitrage price and the clear results are derived in the Markovian case

Low Back Pain Assessment Based on Alpha Oscillation Changes in Spontaneous Electroencephalogram (EEG)

Objectively and accurately assessing pain in clinical settings is challenging. Previous studies showed that alpha oscillations of electroencephalogram data are correlated with subjective perceived pain. Based on this finding, this study is aimed at assessing chronic low back pain based on alpha oscillations. Multichannel electroencephalogram data were recorded from 27 subjects with chronic low back pain under the simple conditions of closing eyes or opening eyes. Spectral analyses were conducted to extract the alpha band responses, and the alpha powers were calculated for the two conditions, respectively. Normalized alpha power was calculated by subtracting the alpha power in the eyes-open condition from that in the eyes-closed condition. The correlation between the alpha power and the subjective pain intensity was evaluated in frontal, central, and posterior regions. The normalized alpha power in the central region was negatively correlated with the subjective pain intensity (R=−0.50, P=0.01), with the strongest correlation occurring at the Cz electrode (R=−0.59, P=0.04). The correlation analysis results demonstrated the possibility of using the differences of alpha spectral power between eyes-closed and eyes-open conditions as a measure for assessing chronic low back pain. The findings suggest that the normalized alpha power in the central region may be used as a measurable and quantitative indicator of chronic pain for clinical applications

Identifying Intraoperative Spinal Cord Injury Location from Somatosensory Evoked Potentials’ Time-Frequency Components

Excessive distraction in corrective spine surgery can lead to iatrogenic distraction spinal cord injury. Diagnosis of the location of the spinal cord injury helps in early removal of the injury source. The time-frequency components of the somatosensory evoked potential have been reported to provide information on the location of spinal cord injury, but most studies have focused on contusion injuries of the cervical spine. In this study, we established 19 rat models of distraction spinal cord injury at different levels and collected the somatosensory evoked potentials of the hindlimb and extracted their time-frequency components. Subsequently, we used k-medoid clustering and naive Bayes to classify spinal cord injury at the C5 and C6 level, as well as spinal cord injury at the cervical, thoracic, and lumbar spine, respectively. The results showed that there was a significant delay in the latency of the time-frequency components distributed between 15 and 30 ms and 50 and 150 Hz in all spinal cord injury groups. The overall classification accuracy was 88.28% and 84.87%. The results demonstrate that the k-medoid clustering and naive Bayes methods are capable of extracting the time-frequency component information depending on the spinal cord injury location and suggest that the somatosensory evoked potential has the potential to diagnose the location of a spinal cord injury