Stochastic Depreciation and Optimal Consumption‐Investment Decisions
将资本积累视为积累与浪费的净结果，用高斯过程建模积累、伪泊松过程建模浪费，推导出包含无穷项的汉密尔顿-雅可比-贝尔曼方程，并展示消费与预期资本浪费的优化过程。
Capital accumulation is viewed as the net outcome of accumulation and wasting. Accumulation is modelled by a Gaussian process whilst wasting is generated by a continuous time and continuous state‐space pseudo‐Poisson process. These assumptions imply that an economic agent’s preferences, consumption, capital accumulation and wastage are governed by a form of Hamilton‐Jacobi‐Bellman equation containing an infinite number of terms. We demonstrate the optimisation procedures applicable to consumption and the expected wastage of capital and in the process show that isoelastic preferences are consistent with the model.