Continuous-time perpetuities and time reversal of diffusions
研究了在遍历马尔可夫模型中估计连续时间永续年金及其现金流率影响因素的联合分布问题，提出了两种方法：偏微分方程法和时间反转法，后者可通过蒙特卡洛模拟高效获取分布。
Abstract We consider the problem of estimating the joint distribution of a continuous-time perpetuity and the underlying factors which govern the cash flow rate, in an ergodic Markovian model. Two approaches are used to obtain the distribution. The first identifies a partial differential equation for the conditional cumulative distribution function of the perpetuity given the initial factor value, which under certain conditions ensures the existence of a density for the perpetuity. The second (and more general) approach, using techniques of time reversal, identifies the joint law as the stationary distribution of an ergodic multidimensional diffusion. This latter approach allows efficient use of Monte Carlo simulation, as the distribution is obtained by sampling a single path of the reversed process.