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This paper proposes two mixed models to study a consumer's optimal saving in the presence of two types of risk., Panoeconomicus, 2017

An intertemporal optimal strategy for accumulation of reversible capital and management of an exhaustible resource is analyzed for a global economy when resource depletion generates discharges that add to a stock pollutant that affects the likelihood for hitting a tipping point or threshold of unknown location, causing a randomdisembodied technical regress. We characterize an optimal strategy by imposing the notion precautionary tax on current extraction for preventing a productivity shock driven by stock pollution and a capital subsidy to promote capital accumulation so as to build up a buffer for future consumption opportunities should the threshold be hit. The precautionary tax will internalize the expected welfare loss should a threshold be hit, whereas the capital subsidy will internalize the expected post-catastrophic long-run return from current capital accumulation.

This paper provides the proofs to the analysis of a continuous time matching model with saving in Bayer and Wälde (2010a). The paper proves the results on consumption growth, provides an existence proof for optimal consumption and a detailed derivation of the Fokker-Planck equations.

Growth models of the Dutch disease, such as those of Krugman (1987), Matsuyama (1992), Sachs and Warner (1995) and Gylfason et al. (1999), explain why resource abundance may reduce growth. The literature, however, also raises a new question: if the use of resource wealth hurts productivity growth, how should such wealth be optimally managed? This question forms the topic of the present paper, in which we extend the growth literature on the Dutch disease from a positive to a normative setting. We show that the assumptions in the previous literature imply that the optimal share of national wealth consumed in each period needs to be adjusted down. Some Dutch disease, however, is always optimal. Thus lower growth in resource abundant countries may not be a problem in itself, but may be part of an optimal growth path. The optimal spending path of the resource wealth may be increasing or decreasing over time, and we discuss why this is the case.

Growth models of the Dutch disease, such as those of Krugman (1987), Matsuyama (1992), Sachs and Warner (1995) and Gylfason et al. (1999), explain why resource abundance may reduce growth. However, the literature also raises a new question: if the use of resource wealth hurts productivity growth, how should such wealth be optimally managed? This question forms the topic of the present paper, in which we extend the growth literature on the Dutch disease from a positive to a normative setting. We show that the assumptions in the previous literature imply that the optimal share of national wealth consumed in each period needs to be adjusted down. However, some Dutch disease is always optimal. Thus lower growth in resource abundant countries may not be a problem in itself, but may be part of an optimal growth path. The optimal spending path of the resource wealth may be increasing or decreasing over time, and we discuss why this is the case.

This paper proposes two mixed models to study optimal saving in the presence of two types of risk: income risk and background risk. In the first model the income risk is a fuzzy number and the background risk is a random variable. In the second model the income risk is a random variable and the background risk is a fuzzy number. For these models three notions of precautionary saving are defined as indicators of the changes induced by the income risk and the background risk on the choice of optimal saving.