Continuous-Time Public Good Contribution under Uncertainty

Ferrari G, Riedel F, Steg J-H (2015) Center for Mathematical Economics Working Papers; 485, Version February 2015.
Bielefeld: Center for Mathematical Economics.

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Abstract
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.
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Ferrari G, Riedel F, Steg J-H. Continuous-Time Public Good Contribution under Uncertainty. Center for Mathematical Economics Working Papers. Vol 485 Version February 2015. Bielefeld: Center for Mathematical Economics; 2015.
Ferrari, G., Riedel, F., & Steg, J. - H. (2015). Continuous-Time Public Good Contribution under Uncertainty (Center for Mathematical Economics Working Papers, 485) Version February 2015. Bielefeld: Center for Mathematical Economics.
Ferrari, G., Riedel, F., and Steg, J. - H. (2015). Continuous-Time Public Good Contribution under Uncertainty. Center for Mathematical Economics Working Papers, 485, Version February 2015. Bielefeld: Center for Mathematical Economics.
Ferrari, G., Riedel, F., & Steg, J.-H., 2015. Continuous-Time Public Good Contribution under Uncertainty, Center for Mathematical Economics Working Papers, no.485, Version February 2015., Bielefeld: Center for Mathematical Economics.
G. Ferrari, F. Riedel, and J.-H. Steg, Continuous-Time Public Good Contribution under Uncertainty, Center for Mathematical Economics Working Papers, vol. 485, Version February 2015., Bielefeld: Center for Mathematical Economics, 2015.
Ferrari, G., Riedel, F., Steg, J.-H.: Continuous-Time Public Good Contribution under Uncertainty. Center for Mathematical Economics Working Papers, 485, Version February 2015. Center for Mathematical Economics, Bielefeld (2015).
Ferrari, Giorgio, Riedel, Frank, and Steg, Jan-Henrik. Continuous-Time Public Good Contribution under Uncertainty. Version February 2015. Bielefeld: Center for Mathematical Economics, 2015. Center for Mathematical Economics Working Papers. 485.
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