Survival Measures and Interacting Intensity Model: with Applications in Guaranteed Debt Pricing

This paper studies survival measures in credit risk models. Survival measure, which was first introduced by Schonbucher [12] in the framework of defaultable LMM, has the advantage of eliminating default indicator variable directly from the expectation by absorbing it into Randon-Nikodym density process. Survival measure approach was further extended by Collin-Duresne[4] to avoid calculating a troublesome jump in IBPR reduced-form model. This paper considers survival measure in "HBPR" model, i.e. default time is characterized by Cox construction, and studies the relevant drift changes and martingale representations. This paper also takes advantage of survival measure to solve the looping default problem in interacting intensity model with stochastic intensities. Guaranteed debt is priced under this model, as an application of survival measure and interacting intensity model. Detailed numerical analysis is performed in this paper to study influence of stochastic pre-default intensities and contagion on value of a two firms' bilateral guaranteed debt portfolio.Survival Measure, Interacting Intensity Model, Measure Change, Guaranteed Debt, Mitigation and Contagion.

Chaos analysis of ship rolling motion in stochastic beam seas

In this paper, the chaotic motion of ship roll in stochastic beam seas, which is regarded as a bounded noise is investigated in detail. The stochastic Melnikov approach is applied to the model and the criterion for the chaos in the mean-square sense is derived. The chaotic thresholds of noise parameters obtained by means of the stochastic Melnikov process are verified by the numerical safe basin. Besides of the factors of noise disturbances, the effects of the other parameters in the system on safe basin are also discussed systematically. The varieties of coefficients of the restoring moment can also induce the erosion of safe basin and lead to the occurrence of the chaos. On the other hand, the increase of damping coefficients can enhance the safe domain of ship sailing

Unilateral CVA for CDS in Contagion model: With volatilities and correlation of spread and interest

The price of financial derivative with unilateral counterparty credit risk can be expressed as the price of an otherwise risk-free derivative minus a credit value adjustment(CVA) component that can be seen as shorting a call option, which is exercised upon default of counterparty, on MtM of the derivative. Therefore, modeling volatility of MtM and default time of counterparty is key to quantification of counterparty risk. This paper models default times of counterparty and reference with a particular contagion model with stochastic intensities that is proposed by Bao et al. 2010. Stochastic interest rate is incorporated as well to account for positive correlation between spread and interest. Survival measure approach is adopted to calculate MtM of risk-free CDS and conditional survival probability of counterparty in defaultable environment. Semi-analytical solution for CVA is attained. Affine specification of intensities and interest rate concludes analytical expression for pre-default value of MtM. Numerical experiments at the last of this paper analyze the impact of contagion, volatility and correlation on CVA.Credit Value Adjustment, Contagion Model, Stochastic Intensities and Interest, Survival Measure, Affine Specification

Stochastic stability and moment Lyapunov exponent for co-dimension two bifurcation system with a bounded noise

In this paper, the pth moment Lyapunov exponent of a co-dimension two bifurcation system that is parametrically excited by a real noise is investigated. By a linear stochastic transformation, the eigenvalue problem of moment Lyapunov exponent is obtained. Then through perturbation method, we deduce the joint probability density function of the phase processes and its eigenvalue problem, which is solved by a Fourier cosine series expansion. Thus, an infinite matrix yields and whose leading eigenvalue is the second order of the asymptotic expansion of the moment Lyapunov exponent. Because of the complexity of elements in matrix A, the eigenvalues of the low order sub-matrices of A are obtained by the truncation of n and the convergence of the eigenvalue sequence is numerically illustrated. Finally, the effects of the system and noise parameters on the moment Lyapunov exponent are discussed

Neuroprotective effects of electro-acupuncture in spinal cord injury rats via up-regulation of DUSP14

Purpose: To study the effect and mechanism of action of electro-acupuncture (EA) on nerve regeneration by analyzing the behavior, inflammation and cell death in spinal cord injury (SCI) rat model. Methods: SCI model was established according to Allen’s falling strike method. Electroacupuncture was performed on Jiaji (EX-B2)/Mingmen (GV4) acupoint with a 1 mA current intermittent wave at a frequency of 2Hz for 20 min daily. Interleukin (IL-6) and tumor necrosis factor-α (TNF-α) levels were measured using ELISA kits. Apoptosis-induced DNA strand breaks were evaluated by TUNEL assay while relative mRNA expression was assessed by quantitative real-time polymerase chain reaction (qRT-PCR). Protein levels were measured by western blot. Results: Relative mRNA and protein expressions of DUSP14 decreased in SCI rats with time but increased by EA treatment. Further, partial locomotor functional recovery was presented in SCI rats by EA treatment. Moreover, intraspinal injection of DUSP14 over-expression viral supernatants/EA treatment ameliorated inflammation and apoptosis in SCI rats. Meanwhile, the protein levels of NF-κB p65 (nucleus) and phosphorylated TGF-activated kinase 1 (p-TAK1) increased in SCI rats following EA treatment but were decreased by EA treatment and intraspinal injection of DUSP14 over-expression viral supernatants. Conclusion: EA acupoint treatment exerts neuroprotective effects in SCI rats via the reduction of inflammation and apoptosis, and induction of DUSP14