A Possibilistic and Probabilistic Approach to Precautionary Saving

Abstract

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.

Key words: Optimal saving, Background risk, Income risk, Possibility theory.
JEL: CO2, D31, D81.

U radu se predlažu dva mešovita modela za proučavanje optimalne štednje potrošača u prisustvu dve vrste rizika: rizik prihoda i eksterni rizik. U prvom modelu, rizik prihoda je predstavljen fazi brojem a eksterni rizik putem slučajne promenljive. U drugom modelu, rizik prihoda je predstavljen putem slučajne promenljive a eksterni rizik putem fazi broja. Za svaki model, tri predpostavke o merama predostrožnosti štednje su definisane kao pokazatelji dodatne štednje izazvane uticajem rizika prihoda i eksternim rizikom na optimalan izbor potrošača. U zaključku, možemo okarakterisati uslove koji omogućavaju dodatnu štednju u odnosu na optimalnu štednju pod sigurnošću, čak i kada se određena komponenta rizika modelira fazi brojevima.

Ključne reči: Optimalna štednja, Eksterni rizik, Rizik prihoda, Teorija mogućnosti.