Year: 2025
Type: preprint
Abstract: We introduce a dynamic model in which a developer incrementally improves a product of uncertain quality over time, with the quality evolving as a controlled Brownian motion. At each moment in time, the developer can continue exploring by paying a flow cost, restart from a previously attained quality level by paying a fixed cost, or terminate the process by either freely abandoning the project or by incurring a cost to launch the highest quality observed so far. The optimal strategy is characterized by a free boundary of an impulse-controlled Brownian motion, reflecting how the developer’s tolerance for setbacks evolves over time in three distinct stages. In the early stage, setbacks lead to project termination; in the intermediate stage, unsuccessful paths serve as learning opportunities, leading to strategic restarts; and in the final stage, the product is inevitably launched, with further improvements enhancing its final quality in a final push. Our model captures the role of active decision-making in managing uncertainty through a true process of trial and error that can be reversed when necessary. The results highlight the essential interplay of persistence and chance, demonstrating that success hinges not only on avoiding prolonged failure but also on the precise timing of interventions.
Source: arXiv (Cornell University)
Author: Oliveros, Santiago
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W4417491566
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