Pricing Catastrophe Options with Credit Risk in a Regime-Switching Model

In this paper,we consider the price of catastrophe options with credit risk in a regime-switching model.We assume that the macroeconomic states are described by a continuous-time Markov chain with a finite state space.By using the measure change technique,we derive the price expressions of catastrophe put options.Moreover,we conduct some numerical analysis to demonstrate how the parameters of the model affect the price of the catastrophe put option.

AN INTEGRATION BY PARTS FORMULA FOR STOCHASTIC HEAT EQUATIONS WITH FRACTIONAL NOISE

In this paper,we establish the integration by parts formula for the solution of fractional noise driven stochastic heat equations using the method of coupling.As an application,we also obtain the shift Harnack inequalities.

A generalization of exotic options pricing formulae

Exotic options, or “path-dependent” options are options whose payoff depends on the behavior of the price of the underlying between 0 and the maturity, rather than merely on the final price of the underlying, such as compound options, reset options and so on. In this paper, a generalization of the Geske formula for compound call options is obtained in the case of time-dependent volatility and time-dependent interest rate by applying martingale methods and the change of numeraire or the change of probability measure. An analytic formula for the reset call options with predetermined dates is also derived in the case by using the same approach. In contrast to partial differential equation (PDE) approach, our approach is simpler.

A model for dependent default with hyperbolic attenuation effect and valuation of credit default swap

A hyperbolic function is introduced to reflect the attenuation effect of one firm＇s default to its partner. If two firms are competitors （copartners）, the default intensity of one firm will decrease （increase） abruptly when the other firm defaults. As time goes on, the impact will decrease gradually until extinct. In this model, the joint distribution and marginal distributions of default times are derived by employing the change of measure, and the fair swap premium of a credit default swap （CDS） can be valued.

PRICING CATASTROPHE OPTIONS WITH COUNTERPARTY CREDIT RISK IN A REDUCED FORM MODEL

In this paper, we study the price of catastrophe Options with counterparty credit risk in a reduced form model. We assume that the loss process is generated by a doubly stochastic Poisson process, the share price process is modeled through a jump-diffusion process which is correlated to the loss process, the interest rate process and the default intensity process are modeled through the Vasicek model： We derive the closed form formulae for pricing catastrophe options in a reduced form model. Furthermore, we make some numerical analysis on the explicit formulae.

Ground characterization and roof mapping: Online sensor signal-based change detection

Measurement while drilling systems are becoming an important part of excavation operations for rock characterization and ground support design that require reliable information on rock strength and location ＆ frequency of joints or voids. This paper focuses on improving rock characterization algorithms for instrumented roof-boRer systems. For this purpose, an improved void detection algorithm is proposed, where the underlying theory is built upon the concept of mean change detection based on the feed pressure signals. In addition, the application of acoustic sensing for void detection is examined and it is shown that the variance of the filtered acoustic signal is correlated to the strength of the material being drilled. The proposed algorithm has been validated on the data collected from full-scale drilling tests in various concrete and rock samples at the J. H. Fletcher facility.

Model of counterparty risk with geometric attenuation and valuation of CDS

To investigate the impact of microstructure interdependency of a counterparty explicitly, a geometric function is introduced in one firm's default intensity to reflect the attenuation behavior of the impact of its counterparty firm's default. The general joint distribution and marginal distributions of default times are derived by employing the change of measure. The fair premium of a vanilla CDS (credit default swap) is obtained in continuous and discrete contexts, respectively. The swap premium in a discrete context is similar to the accumulated interest during the period between two payment days, and the short rate is the swap rate in a continuous context.

Coseismic gravity and displacement changes of Japan Tohoku earthquake(Mw 9.0)

The greatest earthquake in the modern history of Japan and probably the fourth greatest in the last 100 years in the world occurred on March 11, 2011 off the Pacific coast of Tohoku.Large tsunami and ground motions caused severe damage in wide areas, particularly many towns along the Pacific coast. So far, gravity change caused by such a great earthquake has been reported for the 1964 Alaska and the 2010 Maule events. However, the spatial-temporal resolution of the gravity data for these cases is insufficient to depict a co-seismic gravity field variation in a spatial scale of a plate subduction zone. Here, we report an unequivocal co-seismic gravity change over the Japanese Island, obtained from a hybrid gravity observation（combined absolute and relative gravity measurements）. The time interval of the observation before and after the earthquake is within 1 year at almost all the observed sites, including 13 absolute and 16 relative measurement sites, which deduced tectonic and environmental contributions to the gravity change. The observed gravity agrees well with the result calculated by a dislocation theory based on a self-gravitating and layered spherical earth model. In this computation, a co-seismic slip distribution is determined by an inversion of Global Positioning System（GPS） data. Of particular interest is that the observed gravity change in some area is negative where a remarkable subsidence is observed by GPS, which can not be explained by simple vertical movement of the crust. This indicated that the mass redistribution in the underground affects the gravity change. This result supports the result that Gravity Recovery and Climate Experiment（GRACE） satellites detected a crustal dilatation due to the 2004 Sumatra earthquake by the terrestrial observation with a higher spatial and temporal resolution.

Fast Fourier Transform Approximation of Foreign Currency Option Pricing Based on Exponential Lévy Model

To study the approximation of foreign currency option prices when the underlying assets＇ price dynamics are described by exponential Lévy processes, the convolution representations for option pricing formulas were given, and then the fast Fourier transform （FFT） algorithm was used to get the approximate values of option prices. Finally, a numerical example was given to demonstrate the calculate steps to the option price by FFT.

Research on the Commutation Revocation

In order to resist some prisoner who have received rewards of commutation to implement some illegal or criminal behavior in the course of imprisonment, the system of commutation revocation must be established, which can advantage imprisonment and reduce the costs of imprisonment. The system of commutation revocation can obey to the criminal policy of temper justice with mercy and the principle of ＂collecting mistakes whenever discovered＂ and obtain the penalty goal of special prevention. In order to protect some prisoner＇ s benefit, the prisoner who be revoked the rewards of commutation can take part in the course of juice, the postbox which be opened only by the NPC and committee must be installed in prison. This will be advantage of some prisoner who be revoked the rewards of commutation appealing to the NPC and committee. Because of weakness of necessarily and execution, the system of commutation revocation cannot be established when the prisoner have been released currently.

Growth Performance of Arsi, Borana, Harar and HF-Crossbred Bulls Finished under Similar Feeding Condition

The study was conducted to evaluate the fattening performance of Arsi, Borana, Harar and Holstein Friesian crossbred bulls finished under a similar feeding condition at the beef farm in Haramaya University. The average daily weight gain of the four breeds ranges from 0.49 to 0.71 kg. Feed conversion efficiency also ranges from 0.11 - 0.15. Simple linear regression models were used to explore the relationship between live body weight change and change in body condition score as well as seven linear body measurements for all age groups. An average change for a unite of body condition score was equivalent to 20.3, 20.61, 22.42 and 27.78 kg for Borana, Arsi, Harar and Holstein Friesian crossbred bulls respectively. Body condition score was significantly influenced by breeds. There was a significant breed by age interaction effect on the initial body condition score of the four breeds. There was a significant and positive strong association between change in body weight and body condition score. There was a significant and strong correlation between change in body weight and change in Total topline, neck length, heart girth, flank circumference and rump length having correlation coefficients ranges from 0.57 to 0.97. A higher net profit of 7380.47 ETB per head was recorded by Borana bulls followed by Harar bulls, Arsi and Holstein Friesian crossbred with net profit of 5406.86, 5193.29 and 3384.98 ETB per head respectively. Borana bulls are more superior in weight gain and net profit. Bodyweight change could be predicted based on body condition score change during the fattening period.

The Spread Speed of Multiple Catalytic Branching Random Walks

In this paper we study the asymptotic behavior of the maximal position of a supercritical multiple catalytic branching random walk(X_(n))on Z.If M_(n) is its maximal position at time n,we prove that there is a constantα>0 such that M_(n)/n converges toαalmost surely on the set of infinite number of visits to the set of catalysts.We also derive the asymptotic law of the centered process M_(n)-αn as n→∞.Our results are similar to those in[13].However,our results are proved under the assumption of finite L log L moment instead of finite second moment.We also study the limit of(X_(n))as a measure-valued Markov process.For any function f with compact support,we prove a strong law of large numbers for the process X_(n)(f).

A rupture blank zone in middle south part of Longmenshan Faults: Effect after Lushan M_s7.0 earthquake of 20 April 2013 in Sichuan, China

On April 20, 2013, the Lushan M^7.0 earthquake struck at the southern part of the Longmenshan fault in the eastern Tibetan Plateau, China. The shear-wave splitting in the crust indicates a connection between the direction of the principal crustal com- pressive stress and the fault orientation in the Longmenshan fault zone. Our relocation analysis of the aftershocks of the Lushan earthquake shows a gap between the location of the rupture zone of the Lushan Ms7.0 earthquake and that of the rup- ture zone of the Wenchuan MsS.0 earthquake. We believe that stress levels in the crust at the rupture gap and its vicinity should be monitored in the immediate future. We suggest using controlled source borehole measurements for this purpose.

Some Results behind Dividend Problems

We consider the basic dividend problem of the compound Poisson model with constant barrier strategy. Some results concealed behind the dividend problem are made explicit in the present work. Different methods and some of which are firstly given in this paper. All these results presented certain direct relationship between some important actuary variables in classical risk theory is also revealed.

A contagion model with Markov regime-switching intensities

We consider a two-dimensional reduced form contagion model with regime-switching interacting default intensities. The model assumes the intensities of the default times are driven by macro-economy described by a homogeneous Markov chain as well as the other default. By using the idea of ＇change of measure＇ and some closed-form formulas for the Laplace transforms of the integrated intensity processes, we derive the two-dimensional conditional and unconditional joint distributions of the default times. Based on these results, we give the explicit formulas for the fair spreads of the first-to-default and second-to-default credit default swaps （CDSs） on two underlyings.

ANALYSIS OF INCOMPLETE STOCK MARKET WITH JUMP-DIFFUSION UNCERTAINTY

This paper studies incomplete stock market that includes discontinuous price processes. The discontinuity is modeled by very general point processes admitting only stochastic intensities. Prices are driven by jump-diffusion uncertainty and have random but predictable jumps. The space of risk-neutral measures that are associated with the market is identified and related to fictitious completions. The construction of replicating portfolios is discussed, and convex duality methods are used to prove existence of optimal consumption and investment policies for a problem of utility maximization.

On Optimal Proportional Reinsurance and Investment in a Hidden Markov Financial Market

This paper investigates the optimal reinsurance and investment in a hidden Markov financial market consisting of non-risky （bond） and risky （stock） asset. We assume that only the price of the risky asset can be observed from the financial market. Suppose that the insurance company can adopt proportional reinsurance and investment in the hidden Markov financial market to reduce risk or increase profit. Our objective is to maximize the expected exponential utility of the terminal wealth of the surplus of the insurance company. By using the filtering theory, we establish the separation principle and reduce the problem to the complete information case. With the help of Girsanov change of measure and the dynamic programming approach, we characterize the value function as the unique solution of a linear parabolic partial differential equation and obtain the Feynman-Kac representation of the value function.