What is the utility curve of a risk seeker?

The Utility Function and Risk-Seekers The utility function is convex for a risk-lover and concave for a risk-averse person (and subsequently linear for a risk-neutral person). Subsequently, it can be understood that the utility function curves in this way depending on the individual’s personal preference towards risk.

How do you know if a utility function is risk-averse?

Risk-Averse: If a person’s utility of the expected value of a gamble is greater than their expected utility from the gamble itself, they are said to be risk-averse.

What is the utility function of a risk-averse person?

People with concave von Neumann-Morgenstern utility functions are known as risk-averse. people—they prefer the expected value of a gamble to the gamble itself. A useful concept is the certainty equivalent of a gamble.

What shape does a risk-averse person’s utility curve take?

concave
Left graph: A risk averse utility function is concave (from below), while a risk loving utility function is convex.

What is a risk neutral utility function?

Risk neutrality is an economic term that describes individuals’ indifference between various levels of risk. In terms of utility theory, a risk-neutral individual’s utility of expected wealth from a lottery is always equal to his or her expected utility of wealth provided by the same lottery.

What does a utility function look like?

A utility function that describes a preference for one bundle of goods (Xa) vs another bundle of goods (Xb) is expressed as U(Xa, Xb). Where there are perfect complements, the utility function is written as U(Xa, Xb) = MIN[Xa, Xb], where the smaller of the two is assigned the function’s value.

What is logarithmic utility function?

In 1738, Daniel Bernoulli [Bernoulli 1738] (for the English translation see [Bernoulli 1954]) introduced the logarithmic utility function (also known as the log utility): u(x) = ln(x) This function is concave, and it yields to the risk aversion. More importantly, it also yields to the diminishing risk aversion.

Is the utility function the indifference curve?

Utility functions have indifference curves too; they are the level curves in the space (x,y) of the three dimensional function U=f(x,y).

What is power utility function?

In economics, the isoelastic function for utility, also known as the isoelastic utility function, or power utility function is used to express utility in terms of consumption or some other economic variable that a decision-maker is concerned with.

How does risk-averse individual’s money income affect total utility function?

In Fig. 17.3 we have drawn a curve OU showing utility function of money income of an individual who is risk-averse. It will be seen from this figure that the slope of total utility function OL; decreases as the money income of the individual increases. Note that we measure money income on the X-axis and utility on the Y-axis.

How many types of utility curves are there in investing?

Generally speaking, there are three types of utility curves that explain the relationship investors have with risk. This type of utility trend is what most individuals experience, according to the study cited above. From a conceptual standpoint, graphing this type of utility would give us the following:

What is the relationship between risk and marginal utility?

In practice, such an investor would continuously take on more risk since this will result in more utility. This type of investing behavior is quite rare. This attitude towards risk would be exponential, meaning that this investor experiences increasing marginal utility. The graph below illustrates this relationship:

When is the expected utility of a function greater than the utility?

For a risk averse decision maker, the expected utility of a function is less than the utility of the expected monetary value. It is also possible for the decision-maker to be risk preferring, at least over some range of the utility function. In its case the expected utility of a function is more than the utility function.