Open-End Fund Investment with Dynamic Fund Flows and Passive Benchmarking: A Continuous-Time Stackelberg Game

This paper develops a stylized continuous-time framework for open-end fund investment in which state-dependent fund flows, passive benchmarking, and strategic manager–investor interaction are modeled jointly. The contribution is not a new Stackelberg solution concept; rather, it is the economic mechanism created by combining a scale-dependent value-added objective with endogenous subscription and redemption jumps. Fund flows are represented by marked compound Poisson processes, and the manager acts as leader while a representative investor chooses participation as a follower. Under bounded controls, bounded Lipschitz jump intensities, admissible jump-size distributions, and strict-concavity conditions, we establish positivity and moment bounds for the state process, provide sufficient conditions for the existence and uniqueness of a Markov feedback Stackelberg equilibrium, and state a jump-diffusion verification theorem. A transparent local feedback approximation and Monte Carlo robustness exercise illustrate how redemption pressure, subscription intensity, jump-size dispersion, benchmark volatility, and risk aversion affect active exposure and terminal fund wealth. The results show that stronger redemption pressure and benchmark-relative risk reduce active positions, whereas subscription incentives increase risk-taking only when expected value added compensates for flow-induced dilution. Within its stated assumptions, the model provides a tractable theoretical benchmark rather than an empirically validated structural model.