On some aspects of survival under production uncertainty

Abstract

In recent years there has emerged a considerable volume of literature which analyzes the possibility of a certain performance index staying above a minimum level over time for an agent who operates in a given stochastic dynamic environment. Thus, one may be interested in the potential ability of an agent to meet a minimum positive "subsistence" consumption level over time or of firms being able to pay out a minimum level of dividend to shareholders or to meet a minimal level of debt service in order to avoid bankruptcy. For a renewable resource which is exploited over time at a rate determined by the market or by the optimal policy of its owner, one can examine the circumstances under which the resource does not become extinct over time. The literature on exhaustible resources has focused on the difficulties of maintaining a positive steady level of consumption in an economy which relies on an exhaustible resource as an essential input in production [see Solow (1974), Cass and Mitra (1991)]. In a model of renewable resource with stochastic and concave production function, where the resource is depleted every time period according to market equilibrium, Mirman and Spulber (1984) derived results on chances of survival for the resource. Majumdar and Radner (1991,1992) consider a dynamic model ?f consumption and investment with production uncertainty, where the agent is required to meet a certain strictly positive consumption level every time period in order to survive. They consider cases where the production function is of the canonical neoclassical type and also the case where it is linear. This framework is close to the classical gambler's ruin problem in probability theory (see Feller (1957), Billingsley (1979)). In a similar framework, Ray (1984) analyzed the survival problem of economic agents who had the option of borrowing and lending over time.