2024/06/24 by Erik Ekström, Ekström, Erik, Yerkin Kitapbayev +5 · 1 voice · 1 citation
Mathematics · #60J60 #93E11 #93E20 #FOS: Mathematics #Optimization and Control (math.OC) #math.OC
paper · pdf · doi:10.48550/arxiv.2406.16493
arxiv published 2024/06/24 · arxiv updated 2026/06/29
We study a model of irreversible investment for a decision-maker who has the possibility to gradually invest in a project with unknown value. In this setting, we introduce and explore a feature of "learning-by-doing", where the learning rate of the unknown project value is increasing in the decision-maker's level of investment in the project. We show that, under some conditions on the functional dependence of the learning rate on the level of investment (the "signal-to-noise" ratio), the optimal strategy is to invest gradually in the project so that a two-dimensional sufficient statistic reflects below a monotone boundary. Moreover, this boundary is characterised as the solution of a differential problem. Finally, we also formulate and solve a discrete version of the problem, which mirrors and complements the continuous version.