Investments with declining cost following a Lévy process
研究了投资成本随时间下降时的最优投资时机与价值，用Lévy过程模拟创新带来的成本下降，给出了计算投资价值和最优时机的通用方法及多个实例。
We consider an optimal investment problem in which the cost of the investment decreases over time. This decrease is modelled using the negative of a non-decreasing Lévy process. The decreasing cost is a way of modelling that innovations drive down the cost of the investment. We present general results on how to compute both the value of the investment, as well as the optimal time at which the investment should be done. Several explicit examples of how different Lévy processes influence the value of the investment are given as illustrations of the general results. The main tools used are fluctuation theory for Lévy processes and inversion of Laplace transforms. When the inversion can be done analytically, we can present analytical solutions where in some cases only numerical solution has previously been known.