We study a continuous-time problem of public good contribution under uncertainty

for an economy with a finite number of agents. Each agent aims to maximize his expected

utility allocating his initial wealth over a given time period between private consumption and

repeated but irreversible contributions to increase the stock of some public good. We study the

corresponding social planner problem and the case of strategic interaction between the agents.

These problems are set up as stochastic control problems with both monotone and classical controls

representing the cumulative contribution into the public good and the consumption of the

private good, respectively. We characterize the optimal investment policies by a set of necessary

and sufficient stochastic Kuhn-Tucker conditions, which in turn allow to identify a universal signal

process that triggers the public good investments. Further we show that our model exhibits

a dynamic free rider effect. We explicitly evaluate it in a symmetric Black-Scholes setting with

Cobb-Douglas utilities and we show that uncertainty and irreversibility of public good provisions

need not affect the degree of free-riding.