The interest rate for saving as a possibilistic risk (original) (raw)
Related papers
A possibilistic and probabilistic approach to precautionary saving
Panoeconomicus, 2017
This paper proposes two mixed models to study a consumer?s optimal saving in the presence of two types of risk: income risk and background risk. In the first model, income risk is represented by a fuzzy number and background risk by a random variable. In the second model, income risk is represented by a random variable and background risk by a fuzzy number. For each model, three notions of precautionary savings are defined as indicators of the extra saving induced by income and background risk on the consumer?s optimal choice. In conclusion, we can characterize the conditions that allow for extra saving relative to optimal saving under certainty, even when a certain component of risk is modelled using fuzzy numbers.
Connecting possibilistic prudence and optimal saving
Ijimai, 2013
In this paper we study the optimal saving problem in the framework of possibility theory. The notion of possibilistic precautionary saving is introduced as a measure of the way the presence of possibilistic risk (represented by a fuzzy number) influences a consumer in establishing the level of optimal saving. The notion of prudence of an agent in the face of possibilistic risk is defined and the equivalence between the prudence condition and a positive possibilistic precautionary saving is proved. Some relations between possibilistic risk aversion, prudence and possibilistic precautionary saving were established.
Optimal Saving by Expected Utility Operators
Axioms, 2020
This paper studies an optimal saving model in which risk is represented by a fuzzy number and the total utility function of the model is defined by an expected utility operator. This model generalizes some existing possibilistic saving models and from them, by a particularization, one can obtain new saving models. In the paper, sufficient conditions are set for the presence of potential risk to increase optimal saving levels and an approximation formula for optimal saving is demonstrated. Particular models for a few concrete expected utility operators are analyzed for triangular fuzzy numbers and CRRA-utility functions.
Saving under uncertainty: A bivariate non-expected utility approach
The GENEVA Papers on Risk and Insurance- …, 1992
We adopt the multivariate non-expected utility approach proposed by Yaari [1986] to provide a characterization of the comparative statics effects of greater risk aversion and of mean-preserving increases in risk on saving and borrowing in the presence of income and interest rate risk. We show that in Yaari's model, it is possible to extend the applicability of the Diamond and Stiglitz [1974] and Kihlstrom and Mirman [1974] (DSKM) single-crossing property to establish a relationship between greater risk aversion and saving (or borrowing) on the basis of the individual's ordinal preferences as long as the two risks are independent. We also demonstrate that the comparative statics effects of a joint mean-preserving increase in random income and interest rate on saving and borrowing can be determined by an extension of the DSKM single-crossing property.
Fuzzy Sets and Systems, 2009
Risk theory is usually developed within probability theory. The aim of this paper is to propose an approach of the risk aversion by possibility theory, initiated by Zadeh in 1978. The main notion studied in this paper is the possibilistic risk premium associated with a fuzzy number A and a utility function u. Under the hypothesis that the utility function u verifies certain hypotheses, one proves a formula to evaluate the possibilistic risk premium in terms of u and of some possibilistic indicators.
Precautionary saving and risk aversion
Economics Letters, 1988
proved that within the anticipated utility framework, a risk averse decision maker will have precautionary saving regardless of the sign of the third derivative of his utility function. In this note we extend (a modification of) this result for an n-period model.
A possibilistic approach to risk aversion
Soft Computing, 2010
In this paper a possibilistic model of risk aversion based on the lower and upper possibilistic expected values of a fuzzy number is studied. Three notions of possibilistic risk premium are defined for which calculation formulae in terms of Arrow–Pratt index and a possibilistic variance are established. A possibilistic version of Pratt theorem is proved.
Risk Aversion through Fuzzy Numbers
2008 First International Conference on Complexity and Intelligence of the Artificial and Natural Complex Systems. Medical Applications of the Complex Systems. Biomedical Computing, 2008
This paper is concerned with an approach of risk aversion by possibility theory. We introduce and study new possibilistic risk indicators.The main notions are the possibilistic risk premium and the possibilistic relative risk premium associated with a fuzzy number and a utility function. We also give formulae for computing them.
Possibilistic risk aversion and its indicators
2012
In the traditional treatment, risk situations are modeled by random variables. This paper focuses on risk situations described by fuzzy numbers. The goal of the paper is to define and characterize possibilistic risk aversion and study some of its indicators.
New results on precautionary saving and nonlinear risks
Journal of Economics, 2022
We study precautionary saving in a two-period model that allows for nonlinear risks and nonseparable preferences. Permitting nonlinear risk effects is important because they are common in the developing world or when worldwide shocks hit economies, like the COVID-19 pandemic. Allowing nonseparable preferences is also important because they admit the incorporation of intergenerational transfer, habit persistence and other specific features of intertemporal decision making. We decompose the risk shock using Davis's (Int Econ Rev 30(1):131-136, 1989) compensation method and analyze the income and substitution effect of an increase in risk. We prove that the substitution effect is always negative and, therefore, the income effect must be positive and larger in size to have a precautionary net effect. We then apply the method to various sources of risk, such as income, interest rate and wealth risk. We analyze the magnitude of each effect and find the conditions required to guarantee precautionary saving in each case. Our results are presented as signs of covariances, which provides a new perspective on precautionary saving. Keywords Precautionary saving Á Nonlinear risk Á Nonseparable preferences Á Increases in risk Á Mean-preserving spreads JEL Classification E21 Á D81 Á D11