real world measure和risk neutral这两种方法有何特点以及区别，他们运用到的场景分别是什么？

不知道你所说的real world measure具体指什么，是什么Numeraire？其实 Risk neutral measure 的wiki 已经讲得很清楚了

Motivating the use of risk-neutral measures

Prices of assets depend crucially on their risk as investors typically demand more profit for bearing more uncertainty. Therefore, today's price of a claim on a risky amount realised tomorrow will generally differ from its expected value. Most commonly, investors are risk-averse and today's price is below the expectation, remunerating those who bear the risk (at least in large financial markets; examples of risk-seeking markets are casinos and lotteries).

To price assets, consequently, the calculated expected values need to be adjusted for an investor's risk preferences (see also Sharpe ratio). Unfortunately, the discount rates would vary between investors and an individual's risk preference is difficult to quantify.

It turns out that in a complete market with no arbitrage opportunities there is an alternative way to do this calculation: Instead of first taking the expectation and then adjusting for an investor's risk preference, one can adjust, once and for all, the probabilities of future outcomes such that they incorporate all investors' risk premia, and then take the expectation under this new probability distribution, the risk-neutral measure. The main benefit stems from the fact that once the risk-neutral probabilities are found, every asset can be priced by simply taking the present value of its expected payoff. Note that if we used the actual real-world probabilities, every security would require a different adjustment (as they differ in riskiness).