# Utility Function from Maximum Entropy Principle

## Abstract

**:**

## 1 Introduction

## 2 The Maximum Entropy Method in Economics

_{i}(ω) if ω is happening. Hence an insurant has insured himself for the price of and receives Y

_{i}(ω) upon occurrence of this event.

_{0}and aggregate risk Z(ω),

## 3 Utility Function

_{i}(W

_{i}). The index i runs over different agents. It is assumed that the utility function has positive first derivative, , to guarantee that the agent desires the profit and negative second derivative, , to restrict it’s avarice (rational agent should be risk averse). The risk aversion parameter, , is also involved in the utility function to scale the agent’s desire in the market with respect to it’s wealth. The market arrives at the equilibrium state upon the agents satisfaction from their trade. In this respect given the equilibrium prices, each agent maximizes utility by choosing his level of Y

_{i}(ω) in each contingency.

_{i}(ω) hence maximizing of the utility function means,

_{i}is a constant value for the i−th agent.

_{i}(ω), up to a constant number since the agent’s wealth remains unaltered.

_{i}(0) = 0 and , the amount of wealth may be rescaled regarding with this assumption. The parameter ξ is used for the rescaled wealth. For constant risk aversion parameter the exponential form for utility function is obtained.

## 4 Conclusion

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Darooneh, A.H.
Utility Function from Maximum Entropy Principle. *Entropy* **2006**, *8*, 18-24.
https://doi.org/10.3390/e8010018

**AMA Style**

Darooneh AH.
Utility Function from Maximum Entropy Principle. *Entropy*. 2006; 8(1):18-24.
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**Chicago/Turabian Style**

Darooneh, Amir H.
2006. "Utility Function from Maximum Entropy Principle" *Entropy* 8, no. 1: 18-24.
https://doi.org/10.3390/e8010018