VALUE-AT-RISK RISK MEASURE: REPRESENTATION, PREDICTION, AND ACCURATION IN COMMONOTONIC RANDOM VARIABLE
Risk is the effect of random event. The resulting effect is expressed in a function called random variable. Every random variable can be constructed commonotonic random variable. Furthermore, the risk prediction is measured using a risk measure, a function that maps a set of random variable to re...
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| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/50087 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Risk is the effect of random event. The resulting effect is expressed in a function
called random variable. Every random variable can be constructed commonotonic
random variable. Furthermore, the risk prediction is measured using a risk measure,
a function that maps a set of random variable to real numbers. The risk measure
used is Value-at-Risk. Analytically, Value-at-Risk can be represented in the survival
function as the realization of random variable where the value of survival is equal
to one minus the confidence level. In addition, Value-at-Risk can also expressed in
distortion function as a distortion risk measure. Prediction of Value-at-Risk can be
obtained by sample quantile method and its accuration can be calculated through
coverage probability. Then, representation, prediction, and accuration of Valueat-
Risk are applied to the modified random variable and commonotonic random
variable. It shows that Value-at-Risk commonotonic random variable is not much
different to Value-at-Risk initial random variable for the sample sizes of 50; 100;
and 5; 000. However, the larger sample size gives coverage probability that is getting
closer to confidence level |
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