隨機最佳化理論在不確定環境下關聯性投資之應用(I)

Abstract

我們第一年主要想探討在多期型外包生產模型中廒商在面對需求不確定性的狀態下會採 取何種資本投資策略。精確地來講，我們想知道的是在有以及沒有外包生產的可能性時，這 間公司的資本投資策略會有何變化。這項研究和目前大多數討論的外包模型之間最大的不同 是在於我們所討論的模型比較強調利用產品創新而得到的“價格提升”的概念，而一般所討論 的模型則是從製成創新而來的“降低成本”的角度來觀察的。我們假設需求的不確定性是個鞅 的情形，而外包產生的原因則是因爲這個無法事先決定的需求量可能比這間廒商自已所能生 產的量爲多，因而迫使廒商尋求外包。在這裡我們想要研究的是，在有外包的情況時整間公 司是否會降低他的資本投資量，但同時卻會提升這家廒商的利潤。而第二年的計畫則是針對 連續性外包生產模型來加以討論。我們希冀可藉由需求不確定性爲幾何布朗運動的假設來解 出一些適當的結果。

This first-year project investigates optimal capital investment in a multi-period framework where a brand-producing firm facing demand uncertainty chooses the capacity investment whit and without the possibility to outsource. An important feature in this model is that we emphasize the “price-raising” aspect of new invention, namely, product innovation leads to a higher selling price, in contrast to the “cost-reducing” effect of process innovation. We consider demand uncertainty that evolves according to a martingale process, and that outsourcing is a costly behavior should in-house capacity be not suffice to the unexpected demand. We aim to show the Pareto-superiority of outsourcing, i.e., the possibility to outsource allows for a greater firm profit than it otherwise would, and that outsourcing leads to a lower in-house investment. The second-year project further studies the above issues in a continuous-time framework where uncertainty evolves according to a geometric Brownian motion.