# Utility function von Neumann Morgenstern

• Felice
In summary, the conversation discusses the need to introduce risk aversion to a financial intermediation model with delegated monitoring to a venture capitalist. This requires a utility function that follows the von Neumann-Morgenstern criteria, including concavity and continuity. The incentive constraint for the entrepreneur is also mentioned, with the equation ph*v >= pl*v + B. The individual is unsure of which utility function to use, suggesting possible options such as U(v)=-exp(-αv) or U(v)=ln(v). They request clarification on the correct solution.
Felice

## Homework Statement

I have a financial intermediation model with delegated monitoring to a venture capitalist. At the moment all participants are risk neutral and i want to introduce risk aversion to the model. Therefore i need a utility function under the von neumann morgenstern criteria, ie. concavity and continous
v= future project realisation
B= private benefits
ph=probability for high effort
pl=probability for low effort

## Homework Equations

incentive constraint of the entrepreneur : ph times v >= pl times v + B

## The Attempt at a Solution

For risk aversion i need to introduce here utility function in a specific form, but i am not sure which to take

. I thought maybe something like:U(v)= - exp(-αv)or U(v)= ln(v)I'm not sure if this is correct, can someone explain the solution to me?

## 1. What is a utility function von Neumann Morgenstern?

A utility function von Neumann Morgenstern is a mathematical function used in decision theory to represent the preferences of an individual or group. It assigns a numerical value to each possible outcome or decision, reflecting the level of satisfaction or desirability associated with that outcome.

## 2. How is a utility function von Neumann Morgenstern used in decision making?

A utility function von Neumann Morgenstern is used to help individuals or groups make decisions by quantifying their preferences and evaluating the expected utility of different choices. It allows decision makers to compare options and choose the one that maximizes their overall satisfaction.

## 3. What is the difference between expected utility and expected value?

Expected utility takes into account not only the potential monetary gains or losses of a decision, but also the individual or group's level of satisfaction with those outcomes. Expected value only considers the monetary outcomes, not the subjective preferences of the decision maker.

## 4. Can a utility function von Neumann Morgenstern accurately represent individual preferences?

While a utility function von Neumann Morgenstern is a useful tool for decision making, it is based on the assumption that individuals are rational and have consistent preferences. In reality, individual preferences may be influenced by emotions, biases, and other factors that cannot be accurately captured by a mathematical function.

## 5. Are there any limitations to using a utility function von Neumann Morgenstern?

Like any mathematical model, a utility function von Neumann Morgenstern has limitations and may not accurately capture the complexities of decision making in real-world scenarios. It also relies on individuals having complete and accurate information, which may not always be the case. Additionally, it does not account for the possibility of unexpected events or outcomes.

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