Minimal entropy martingale measure
Okay kiddo, let me try to explain what minimal entropy martingale measure is in a way that makes sense to a 5-year-old.
Imagine you have a toy car that moves from one place to another over time. Now, let's say you have a bunch of people, each with their own predictions about where the toy car will be at different times. But, because we can't see the future, we don't know for sure which prediction is correct.
Now, imagine there is a way to figure out which person's predictions are the most accurate. This would be really helpful, right? This is sort of what the minimal entropy martingale measure does.
Instead of a toy car, we have something called a financial market, which is made up of stocks, bonds, and other things that people invest in. Just like with the toy car, there are a lot of people who have their own predictions about how the financial market will behave over time.
But, we want to know whose predictions are the most accurate. This is where the minimal entropy martingale measure comes in. This measure helps us figure out which prediction is most likely to be correct.
It does this by looking at all the different predictions made by everyone and finding the one that matches the actual behavior of the financial market the best. It then assigns a probability to each prediction and uses the one with the highest probability as the most accurate.
The reason it's called a "minimal entropy" measure is because it tries to minimize the uncertainty or randomness involved in predicting how the financial market will behave over time.
So, in summary, the minimal entropy martingale measure helps us figure out whose predictions about the financial market are the most accurate by looking at all the different predictions and finding the one that matches the actual behavior of the market the best.
Imagine you have a toy car that moves from one place to another over time. Now, let's say you have a bunch of people, each with their own predictions about where the toy car will be at different times. But, because we can't see the future, we don't know for sure which prediction is correct.
Now, imagine there is a way to figure out which person's predictions are the most accurate. This would be really helpful, right? This is sort of what the minimal entropy martingale measure does.
Instead of a toy car, we have something called a financial market, which is made up of stocks, bonds, and other things that people invest in. Just like with the toy car, there are a lot of people who have their own predictions about how the financial market will behave over time.
But, we want to know whose predictions are the most accurate. This is where the minimal entropy martingale measure comes in. This measure helps us figure out which prediction is most likely to be correct.
It does this by looking at all the different predictions made by everyone and finding the one that matches the actual behavior of the financial market the best. It then assigns a probability to each prediction and uses the one with the highest probability as the most accurate.
The reason it's called a "minimal entropy" measure is because it tries to minimize the uncertainty or randomness involved in predicting how the financial market will behave over time.
So, in summary, the minimal entropy martingale measure helps us figure out whose predictions about the financial market are the most accurate by looking at all the different predictions and finding the one that matches the actual behavior of the market the best.