TL;DR
This paper presents a dynamic model of product development where a developer incrementally improves a product's uncertain quality over time, balancing exploration, restarting, or terminating, with the optimal strategy characterized by impulse control theory.
Contribution
It introduces a novel stochastic control model for product development with a free boundary solution, combining exploration, restart, and termination decisions.
Findings
Optimal strategy characterized by a free boundary of impulse-controlled Brownian motion.
Provides a mathematical framework for decision-making in incremental product improvement.
Analyzes trade-offs between exploration, restarting, and termination in uncertain quality evolution.
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.
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