In this paper, we consider a Markov switching Lévy process model in which the underlying risky assets are driven by the stochastic exponential of Markov switching Lévy process and then apply the model to opt...In this paper, we consider a Markov switching Lévy process model in which the underlying risky assets are driven by the stochastic exponential of Markov switching Lévy process and then apply the model to option pricing and hedging. In this model, the market interest rate, the volatility of the underlying risky assets and the N-state compensator,depend on unobservable states of the economy which are modeled by a continuous-time Hidden Markov process. We use the MEMM(minimal entropy martingale measure) as the equivalent martingale measure. The option price using this model is obtained by the Fourier transform method. We obtain a closed-form solution for the hedge ratio by applying the local risk minimizing hedging.展开更多
Software maintainability is one of the most important factors of software quality,but it is seriously difficult to evaluate the maintainability. Without evaluation,it is impossible to control. To estimate software mai...Software maintainability is one of the most important factors of software quality,but it is seriously difficult to evaluate the maintainability. Without evaluation,it is impossible to control. To estimate software maintainability state,parameter system of software was built up and maintainability state was defined into three states.Thought of application on maintainability evaluation based on hidden Markov chain( HMC) and fuzzy inference was presented.Three-state maintainability estimation model was constructed. To testify the feasibility of the model, a real example of software maintenance activity was carried out and the result from the example validated that the results of this study were applicable.展开更多
This work concerns Lotka–Volterra models that are formulated using stochastic differential equations with regime-switching.Distinct from the existing formulations,the Markov chain that models random environments is u...This work concerns Lotka–Volterra models that are formulated using stochastic differential equations with regime-switching.Distinct from the existing formulations,the Markov chain that models random environments is unobservable.For such partially observed systems,we use Wonham’s filter to estimate the Markov chain from the observable evolution of the population,and convert the original system to a completely observable one.We then show that the positive solution of our model does not explode in finite time with probability 1.Several properties including stochastic boundedness,finite moments,sample path continuity and large-time asymptotic behaviour are also obtained.Moreover,stochastic permanence,extinction and feedback controls are also investigated.展开更多
基金Supported by the National Natural Science Foundation of China(11201221)Supported by the Natural Science Foundation of Jiangsu Province(BK2012468)
文摘In this paper, we consider a Markov switching Lévy process model in which the underlying risky assets are driven by the stochastic exponential of Markov switching Lévy process and then apply the model to option pricing and hedging. In this model, the market interest rate, the volatility of the underlying risky assets and the N-state compensator,depend on unobservable states of the economy which are modeled by a continuous-time Hidden Markov process. We use the MEMM(minimal entropy martingale measure) as the equivalent martingale measure. The option price using this model is obtained by the Fourier transform method. We obtain a closed-form solution for the hedge ratio by applying the local risk minimizing hedging.
文摘Software maintainability is one of the most important factors of software quality,but it is seriously difficult to evaluate the maintainability. Without evaluation,it is impossible to control. To estimate software maintainability state,parameter system of software was built up and maintainability state was defined into three states.Thought of application on maintainability evaluation based on hidden Markov chain( HMC) and fuzzy inference was presented.Three-state maintainability estimation model was constructed. To testify the feasibility of the model, a real example of software maintenance activity was carried out and the result from the example validated that the results of this study were applicable.
基金This work was supported in part by the National Science Foundation under DMS-1207667.
文摘This work concerns Lotka–Volterra models that are formulated using stochastic differential equations with regime-switching.Distinct from the existing formulations,the Markov chain that models random environments is unobservable.For such partially observed systems,we use Wonham’s filter to estimate the Markov chain from the observable evolution of the population,and convert the original system to a completely observable one.We then show that the positive solution of our model does not explode in finite time with probability 1.Several properties including stochastic boundedness,finite moments,sample path continuity and large-time asymptotic behaviour are also obtained.Moreover,stochastic permanence,extinction and feedback controls are also investigated.
