Banking institutions all over the world face significant challenge due to the cumulative loss due to defaults of borrowers of different types of loans. The cumulative default loss built up over a period of time could ...Banking institutions all over the world face significant challenge due to the cumulative loss due to defaults of borrowers of different types of loans. The cumulative default loss built up over a period of time could wipe out the capital cushion of the banks. The aim of this paper is to help the banks to forecast the cumulative loss and its volatility. Defaulting amounts are random and defaults occur at random instants of time. A non Markovian time dependent random point process is used to model the cumulative loss. The expected loss and volatility are evaluated analytically. They are functions of probability of default, probability of loss amount, recovery rate and time. Probability of default being the important contributor is evaluated using Hidden Markov modeling. Numerical results obtained validate the model.展开更多
The remain passenger problem at subway station platform was defined initially,and the period variation of remain passenger queues at platform was investigated through arriving and boarding analyses.Taking remain passe...The remain passenger problem at subway station platform was defined initially,and the period variation of remain passenger queues at platform was investigated through arriving and boarding analyses.Taking remain passenger queues at platform as dynamic stochastic process,a new probabilistic queuing method was developed based on probabilistic theory and discrete time Markov chain theory.This model can calculate remain passenger queues while considering different directions.Considering the stable or variable train arriving period and different platform crossing types,a series of model deformation research was carried out.The probabilistic approach allows to capture the cyclic behavior of queues,measures the uncertainty of a queue state prediction by computing the evolution of its probability in time,and gives any temporal distribution of the arrivals.Compared with the actual data,the deviation of experimental results is less than 20%,which shows the efficiency of probabilistic approach clearly.展开更多
文摘Banking institutions all over the world face significant challenge due to the cumulative loss due to defaults of borrowers of different types of loans. The cumulative default loss built up over a period of time could wipe out the capital cushion of the banks. The aim of this paper is to help the banks to forecast the cumulative loss and its volatility. Defaulting amounts are random and defaults occur at random instants of time. A non Markovian time dependent random point process is used to model the cumulative loss. The expected loss and volatility are evaluated analytically. They are functions of probability of default, probability of loss amount, recovery rate and time. Probability of default being the important contributor is evaluated using Hidden Markov modeling. Numerical results obtained validate the model.
基金Project(2011BAG01B01) supported by the Major State Basic Research and Development Program of ChinaProject(RCS2012ZZ002) supported by the State Key Lab of Rail Traffic Control and Safety,China
文摘The remain passenger problem at subway station platform was defined initially,and the period variation of remain passenger queues at platform was investigated through arriving and boarding analyses.Taking remain passenger queues at platform as dynamic stochastic process,a new probabilistic queuing method was developed based on probabilistic theory and discrete time Markov chain theory.This model can calculate remain passenger queues while considering different directions.Considering the stable or variable train arriving period and different platform crossing types,a series of model deformation research was carried out.The probabilistic approach allows to capture the cyclic behavior of queues,measures the uncertainty of a queue state prediction by computing the evolution of its probability in time,and gives any temporal distribution of the arrivals.Compared with the actual data,the deviation of experimental results is less than 20%,which shows the efficiency of probabilistic approach clearly.
