A Multigenerational Game Model to Analyze Sustainable Development

This paper deals with a multigeneration game that provides a new rationale for representing time preference in very long term cost benefit analysis, as it happens typically in the economics of global climate change. One defines an intergenerational game where each generation has a random life duration and transfers the control of the economic system to the next generation at the end of its life. The payoff to a generation is a discounted sum of the expected consumption by the whole infinite sequence of generations, starting with the current one. The equilibrium is characterized by a dynamic programming equation; a unique solution is proved to exist; a numerical technique is proposed and implemented on a continuous time simplified version of the model DICE94. The results show the influence of this form of altruism on the asymptotic steady states of the economy subject to a global climate change effec

Optimal Conservation Policy under Imperfect Intergenerational Altruism

In this paper we study the optimal forest conservation policy by a hyperbolically discounting society. Society comprises a series of non-overlapping imperfectly altruistic generations each represented by its own government. Under uncertainty about future pay-offs we determine, as solution of an intergenerational dynamic game, the optimal timing of irreversible harvest. Earlier harvest occurs and the option value attached to the forest clearing decision is eroded under both the assumptions of naïve and sophisticated belief about future time-preferences. This results in a bias toward the current generation gratification which affects the intergenerational allocation of benefits and costs from harvesting and conserving a natural forest.Imperfect altruism, Real Options, Hyperbolic Discounting, Time Inconsistency, Natural Resources Management, Resource /Energy Economics and Policy, D81, C70, Q23, Q58,

Quantifying and managing uncertainty in piecewise-deterministic Markov processes

In piecewise-deterministic Markov processes (PDMP) the state of a finite-dimensional system evolves dynamically, but the evolutive equation may change randomly as a result of discrete switches. A running cost is integrated along the corresponding piecewise-deterministic trajectory up to the termination to produce the cumulative cost of the process. We address three natural questions related to uncertainty in cumulative cost of PDMP models: (1) how to compute the Cumulative Distribution Function (CDF) when the switching rates are fully known; (2) how to accurately bound the CDF when the switching rates are uncertain; and (3) assuming the PDMP is controlled, how to select a control to optimize that CDF. In all three cases, our approach requires posing a (weakly-coupled) system of suitable hyperbolic partial differential equations, which are then solved numerically on an augmented state space. We illustrate our method using simple examples of trajectory planning under uncertainty.Comment: submitted to SIAM/ASA Journal on Uncertainty Quantificatio

A stochastic control model of economic growth with environmental disaster prevention

This paper proposes a capital accumulation model with a random stopping time corresponding to the occurrence of an environmental catastrophe. Depending on the preventive capital stock accumulated at the time of the catastrophe, the damage cost associated with the catastrophe varies. The long-term behavior of the optimal accumulation path is analyzed using turnpike theory. The case where the catastrophe process is uncontrolled is distinguished from the case where there is an anthropogenic effect on the probability of an occurrence. Intergenerational equity issues are discussed. Numerical experiments with an adaptation of the integrated assessment model DICE94 are proposed to explore the model responses