大阪大学　数理・データ科学教育研究センター
Center for Mathematical Modeling and Data Science,The University of Osaka

Certainty equivalent and uncertainty premium of time-to-build

Haejun Jeon (The University of Osaka)

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4. Certainty equivalent and uncertainty premium of time-to-build

UQ-Osaka Seminar on Financial Mathematics and Economics 第５回 (University of QueenslandとMMDS金融保険部門共催)

Certainty equivalent and uncertainty premium of time-to-build

Haejun Jeon (The University of Osaka)

Time-to-build of an investment project induces a discrepancy between the timing of investment and that of revenue generation. Jeon (2024) showed that uncertainty in the time-to-build always accelerates investment and enhances pre-investment firm value, regardless of its distribution. This study examines the extent to which the uncertainty advances the timing of investment and improves firm value. Specifically, we show that there always exists a unique certainty equivalent of uncertain time-to-build and derive it in an analytic form. This enables us to derive the investment strategy with uncertain time-to-build in the form of the one that would have been adopted in the absence of such uncertainty. Even without full knowledge of the uncertainty, the firm can approximate the optimal investment strategy using only the mean and variance of time-to-build. We also clarify the positive impact of entropic risk measure of time-to-build on investment and derive the dual representation of the certainty equivalent of time-to-build based on relative entropy. Furthermore, we show that there always exists an uncertainty equivalent of fixed time-to-build. This implies that the firm can deduce the equivalent risk that its investment strategy, established without considering uncertainty in time-to-build, implicitly assumes. Lastly, we illustrate the practical application of our findings using some representative probability distributions and analyze the effects of the variance of time-to-build. In particular, we contrast the effects of uncertainty in demand with those of uncertainty in time-to-build, deriving the level of variance in time-to-build that offsets the negative impact of increased demand volatility on investment. Joint work with Michi Nishihara (University of Osaka).