The interest rate for saving as a possibilistic risk

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.

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.

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.

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.

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.

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

Economics Letters, 2010

Risk may induce precautionary saving but it can also reduce saving. The theoretical literature recognizes both possibilities, but favors a positive effect (both for developed and developing countries); the empirical literature is divided, reporting (small) positive effects for developed economies and (large) negative effects for developing countries. We show in a 2-period model how the effect of risk on savings depends not only on preferences but also on the type of risk.

Fuzzy Sets and Systems, 2016

In this paper, we generalize classical results on risk aversion by analyzing the case, when the available data about cash flows are fuzzy numbers, random fuzzy numbers, type-2 fuzzy sets, random type-2 fuzzy sets etc. We prove that the Arrow-Pratt measures are also risk aversion measures when an agent measures her risk using the Jensen-type operators. We also provide numerous examples of the Jensen-type operators.

Economics Bulletin, 2007

The aim of this note is to suggest that prudence, i.e. convexity of marginal utility, can only explain a small share of precautionary savings, which we may define as savings generated by variance in income. Therefore, if we are willing to admit that precautionary savings constitute a sizable share of total savings, other factors should be called for. We present a few examples showing that risk aversion might constitute one such factor.

German Economic Review, 2005

This paper develops a model of personal saving that includes, unlike previous models appearing in the literature, an explicit role for the Leland-Kimball measure of prudence. Estimation of the model using Bank of Italy survey data suggests that a large share of total saving is driven by precautionary reasons.

Journal of Monetary Economics, 2008

This paper examines how stochastic changes in risk a¤ect the demand for saving. We consider two models of savings demand: one in which future labor income is risky and one in which the return on savings is risky. In each model, we examine the e¤ects of an N th-degree stochastic change in the risk. For each case, we establish necessary and su¢ cient conditions on preferences that will guarantee that the individual increases his or her level of savings. We show how in the case of only labor income risk, any changes in savings are purely due to precautionary savings motives. For the case where the return on savings is risky, we show how both a precautionary e¤ect and a substitution e¤ect need to be analyzed.

Economics Letters, 2014

2020

We study precautionary saving in a two-period model using Davis’s(1989) compensation method, which allows a separation between income and substitution effect when the decision maker faces an increase in risk. We prove that the substitution effect is always negative and therefore, the income effect must then be positive and larger in size to have an increase in saving or a precautionary effect. We then apply the method to different sources of risks like income, interest rate and wealth risk and analyze the magnitude of each effect and find the conditions required to guarantee precautionary saving in each case. We observe that when the utility function is time separable, the conditions to have precautionary effect are the ones we know from the literature. However, our more general setting allows for the possibility of non-linear risk effects. Our results are presented as signs of covariances, which provide a new perspective on the issue of precautionary saving. The authors acknowledge...

2019

The article is devoted to risk modeling in prudent operators or investors, whose decisions are characterized by a trade-off between loss risk and reproduction function. Their attitude may be covered by the combined use of quantitative risk measures. Show the approach to risk modeling, which we will move to the traditional theory of maximizing the possibility of using service functions. Investors who engage their capital are always at risk because they make changes in the structure of their assets when investing. The risk of investing is identified with a possible threat or chance of achieving the expected benefits and is associated with the risk of an investment effect not being expected. This effect may be worse or better than previously assumed. The need to identify and verify the risk results from the possibility of achieving the expected benefits of the investor or avoiding losses. When making investment decisions, we can distinguish three types of investor behavior: Preference for risk and its effects (gambler)the investor makes decisions even when the probability of loss exceeds the probability of profit. The investor is willing to incur higher expenses in order to make a decision about a higher risk. Risk neutrality-the investor does not make decisions when the probability of making a profit is too low. When making decisions, the investor does not pay attention to the amount of risk. Risk aversion-the investor expects the probability of profit to be greater than loss. An investor takes a risk when he expects to receive bonus compensation. Risk aversion also depends on the investor's resources. The richer the investor, the easier it will be for him to accept the loss. The models described in the article assume that investors act rationally and are characterized by risk aversion.

Journal of Economic Dynamics and Control, 1998

This paper considers the problem of precautionary savings for an expected utility specification with finite horizon. The exact solution is known for only a few cases. Numerical methods have limited applications because of Bellman's 'curse of dimensionality'. This paper derives a simple analytical approximate solution for a general specification of the felicity function which is linear in the variance of the innovations on human wealth. Numerically, the approximation is very accurate for realistic values of the parameters of the problem.