Optimal investment timing and size decision‐making with jump risk and time‐inconsistent preferences

Abstract

This paper analyzes a firm's investment timing and capacity decision by considering the manager's time‐inconsistent preferences and continuous economic depreciation of the capital stock cannot be completely offset. The demand shock of the underlying product evolves according to a double exponential jump‐diffusion process. Within a real options framework, we derive the explicit expressions for the optimal investment threshold and investment size when the manager is sophisticated. We find that time‐inconsistent preferences will lead the firm to delay investment when capital depreciation rate is low and accelerate investment when the rate of capital depreciation is high. Further, we show that capital depreciation rate has a monotonic positive effect on the investment size of a time‐consistent manager but a non‐monotonic effect on that of a sophisticated manager. A sophisticated manager tends to choose a smaller investment size than a time‐consistent manager. Finally, we demonstrate that compared with the geometric Brownian motion, the firm invests later with a larger capacity under the jump‐diffusion model.