Abstract:

In practice， investors must continuously update their beliefs about project quality through costly information acquisition， and they actively incorporate behavioral preferences toward risk and uncertainty into their decision-making. A unified analytical framework is developed that integrates Bayesian learning and prospect theory to study optimal venture capital investment timing in a dynamic setting. Research background In the post-pandemic era， venture capital markets have been facing increasing uncertainty due to macroeconomic fluctuations， monetary tightening， and geopolitical risks. Venture capital projects are typically characterized by long investment horizons and severe information incompleteness， making optimal investment timing a crucial determinant of investment performance. The optimal investment timing decision of venture capital projects is studied under incomplete information. The investor does not directly observe the true success probability of the project but forms a Bayesian posterior belief {\pi }_t through continuous information collection. The investor must decide whether to invest immediately or delay investment while updating beliefs， taking into account information costs and uncertainty.Research methods and models， the irreversible investment decision is modeled as an optimal stopping problem under uncertainty. The project’s investment prospect evolves stochastically， and the Bayesian posterior belief follows a learning process with mode-specific information quality and acquisition costs. Prospect theory is incorporated to describe investors’ reference-dependent preferences and asymmetric attitudes toward gains and losses. The decision problem is formulated using a Hamilton–Jacobi–Bellman （HJB） equation.The results indicate that optimal investment timing follows a belief threshold， at which the investor is indifferent between immediate and delayed investment. Under the delayed investment strategy， both the expected value and the choice of learning mode are jointly affected by information volatility and the discount rate. Higher information volatility， which reduces information quality， raises the investment threshold and leads to delayed investment. Conversely， a lower discount rate induces investors to control information acquisition costs by choosing low-cost learning modes and postponing investment. Numerical simulations are conducted using parameter values commonly adopted in the venture capital literature. The simulation results are consistent with the theoretical analysis and illustrate the effects of information volatility and discount rates on investment timing.Bayesian learning and prospect theory are integrated into a unified dynamic investment timing framework， offering a coherent explanation of how belief updating， behavioral preferences， and learning costs jointly determine venture capital investment timing in highly uncertain environments.

Key words: prospect theory, Bayesian posterior beliefs, learning mode, optimal investment timing