Financial mathematics problems

Risk aversion: a person's preference when taking risks. It can be used to measure people's willingness to pay to reduce the risks they face. In the process of weighing the costs and benefits of reducing risks, risk averse people tend to make low-risk choices at the same cost. For example, if you are usually willing to accept a lower expected rate of return on an investment because this rate of return is more predictable, you are a risk averse. When choosing investment projects with the same expected rate of return, risk averse people generally choose the projects with the lowest risk.

The above is the definition of risk aversion

It can be seen that this person's investment behavior tends to be the lowest risk under the maximization of utility.

Let's calculate several mathematical expectations.

1. In his opinion, if he accepts some kind of lottery, he can win the 200 yuan with a probability of %50 and lose 100 yuan with a probability of %50, so this result has no effect on his utility.

Mathematical expectation e1= 200 * 50%-100 * 50% = 50 yuan.

2. In addition, in his view, if there are two choices,

1.300 represents a 50% probability, and 0 represents a 50% probability.

2, stable to 100 yuan

He thinks the two choices make no difference to him.

Mathematical expectations are E2 = 150 and E3 = 100 (certainty) respectively.

Then set a utility function, and then discuss it!

It seems that it won't be done next. Finance has been lost 1000 years!