Modeling log-mortality rates on O-U type processes and forecasting life expectancies are explored using U.S. data. In the classic Lee-Carter model of mortality, the time trend and the age-specific pattern of mortality...Modeling log-mortality rates on O-U type processes and forecasting life expectancies are explored using U.S. data. In the classic Lee-Carter model of mortality, the time trend and the age-specific pattern of mortality over age group are linear, this is not the feature of mortality model. To avoid this disadvantage, O-U type processes will be used to model the log-mortality in this paper. In fact, this model is an AR(1) process, but with a nonlinear time drift term.Based on the mortality data of America from Human Mortality database(HMD), mortality projection consistently indicates a preference for mortality with O-U type processes over those with the classical Lee-Carter model. By means of this model, the low bounds of mortality rates at every age are given. Therefore, lengthening of maximum life expectancies span is estimated in this paper.展开更多
Ornstein-Uhlenbeck superprocess (O-U superprocess for short) first given in ref. [1], is a Gaussian Markov process with values in Schwartz distributions. The background for this process is as the fluctuation limit of ...Ornstein-Uhlenbeck superprocess (O-U superprocess for short) first given in ref. [1], is a Gaussian Markov process with values in Schwartz distributions. The background for this process is as the fluctuation limit of some rescaled particle system, and describes the fluctuation of particle system around its macroscopic flow. Since O-U superprocess can be identified with the solution of some generalized Langevin equation, it is a kind of展开更多
This paper studies hypothesis testing in the Ornstein-Ulenbeck process with linear drift. With the help of large and moderate deviations for the log-likelihood ratio process, the decision regions and the corresponding...This paper studies hypothesis testing in the Ornstein-Ulenbeck process with linear drift. With the help of large and moderate deviations for the log-likelihood ratio process, the decision regions and the corresponding decay rates of the error probabilities related to this testing problem are established.展开更多
In this paper, we study the upper bounds for ruin probabilities of an insurance company which invests its wealth in a stock and a bond. We assume that the interest rate of the bond is stochastic and it is described by...In this paper, we study the upper bounds for ruin probabilities of an insurance company which invests its wealth in a stock and a bond. We assume that the interest rate of the bond is stochastic and it is described by a Cox-Ingersoll-Ross （CIR） model. For the stock price process, we consider both the case of constant volatility （driven by an O U process） and the case of stochastic volatility （driven by a CIR model）. In each case, under certain conditions, we obtain the minimal upper bound for ruin probability as well as the corresponding optimal investment strategy by a pure probabilistic method.展开更多
基金Supported by National Social Science Fund of China(17BTJ023)
文摘Modeling log-mortality rates on O-U type processes and forecasting life expectancies are explored using U.S. data. In the classic Lee-Carter model of mortality, the time trend and the age-specific pattern of mortality over age group are linear, this is not the feature of mortality model. To avoid this disadvantage, O-U type processes will be used to model the log-mortality in this paper. In fact, this model is an AR(1) process, but with a nonlinear time drift term.Based on the mortality data of America from Human Mortality database(HMD), mortality projection consistently indicates a preference for mortality with O-U type processes over those with the classical Lee-Carter model. By means of this model, the low bounds of mortality rates at every age are given. Therefore, lengthening of maximum life expectancies span is estimated in this paper.
文摘Ornstein-Uhlenbeck superprocess (O-U superprocess for short) first given in ref. [1], is a Gaussian Markov process with values in Schwartz distributions. The background for this process is as the fluctuation limit of some rescaled particle system, and describes the fluctuation of particle system around its macroscopic flow. Since O-U superprocess can be identified with the solution of some generalized Langevin equation, it is a kind of
文摘This paper studies hypothesis testing in the Ornstein-Ulenbeck process with linear drift. With the help of large and moderate deviations for the log-likelihood ratio process, the decision regions and the corresponding decay rates of the error probabilities related to this testing problem are established.
基金Supported by National Basic Research Program of China (973 Program, Grant No. 2007CB814905)National Natural Science Foundation of China (Grant No. 10871102)
文摘In this paper, we study the upper bounds for ruin probabilities of an insurance company which invests its wealth in a stock and a bond. We assume that the interest rate of the bond is stochastic and it is described by a Cox-Ingersoll-Ross （CIR） model. For the stock price process, we consider both the case of constant volatility （driven by an O U process） and the case of stochastic volatility （driven by a CIR model）. In each case, under certain conditions, we obtain the minimal upper bound for ruin probability as well as the corresponding optimal investment strategy by a pure probabilistic method.
