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hbc0728 · 2021年08月07日

不是n越大,越趋近于GDP吗?

NO.PZ2018122701000030

问题如下:

Let X be a random variable representing the daily loss of your portfolio. The "peaks over threshold" (POT) approach considers a threshold value, u, of X and the distribution of excess losses over this threshold. Which of the following statements about this application of extreme value theory is correct?

选项:

A.

To apply the POT approach, the distribution of X must be elliptical and known.

B.

If X is normally distributed, the distribution of excess losses requires the estimation of only one parameter, β, which is a positive scale parameter.

C.

To apply the POT approach, one must choose a threshold, u, which is high enough that the number of observations in excess of u is zero.

D.

As the threshold, u, increases, the distribution of excess losses over u converges to a generalized Pareto distribution.

解释:

D is correct.

考点: Extreme Value

解析: The distribution of excess losses over u converges to a generalized Pareto distribution as the threshold value u increases.

The distribution of X itself can be any of the commonly used distribution: normal, lognormal, t, etc., and will usually be known. The distribution of excess losses requires the estimation of two parameters, a positive scale parameter β and a shape or tail index parameter ξ. One must choose a threshold u that is high enough so that the theory applies but also low enough so that there are observations in excess of u.

不是n越大,越趋近于GDP吗?

1 个答案

品职答疑小助手雍 · 2021年08月07日

嗨,爱思考的PZer你好:


是threshold要足够高才能趋近GDP,讲义44页。

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NO.PZ2018122701000030

2022-01-22 18:15 1 · 回答

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