## Abstract

Information related to the tail of loss distribution especially its variability is vital since tail of distribution is related to big losses and overall risk. Risk measure that is commonly used is Tail Conditional Expectation (TCE) that measures expectation of loss that possibly occur given loss exceeded certain percentiles. However, TCE could not describe clearly the behavior and variability of loss along its tail since it only provides measure of central tendency. Additional information is needed to describe variability of loss, for instance measure of dispersion. In this paper will be discussed further about risk and variability measurement named Tail Variance Premium (TVP) and Tail Standard Deviation Premium (TSDP). They are combination of both central tendency and dispersion statistics, so they can measure variability of loss along the right tail better. TVP and TSDP could be alternative risk measure, especially when risk that is bigger than a certain threshold is concerned. Besides, we will also discuss the criteria satisfied by both risk measures with the proof for each criterion. Next, we also provide the explicit formula of TVP and TSDP for loss with normal distribution in particular. Then we will perform calculation for risk measurement of a stock, both by parametric and non-parametric method. We also show the comparison of risk measurement generated by Value-at-Risk, TCE, TVP, and TSDP.

Original language | English |
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Title of host publication | Proceedings of the International Conference on Mathematical Sciences and Technology 2018, MathTech 2018 |

Subtitle of host publication | Innovative Technologies for Mathematics and Mathematics for Technological Innovation |

Editors | Yazariah Mohd Yatim, Syakila Ahmad, Mohd Tahir Ismail, Majid Khan Majahar Ali, Rosmanjawati Abdul Rahman, Hajar Sulaiman, Norshafira Ramli, Noor Atinah Ahmad, Farah Aini Abdullah |

Publisher | American Institute of Physics Inc. |

ISBN (Electronic) | 9780735419315 |

DOIs | |

Publication status | Published - 4 Dec 2019 |

Event | 1st International Conference on Mathematical Sciences and Technology 2018: Innovative Technologies for Mathematics and Mathematics for Technological Innovation, MathTech 2018 - Penang, Malaysia Duration: 10 Dec 2018 → 12 Dec 2018 |

### Publication series

Name | AIP Conference Proceedings |
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Volume | 2184 |

ISSN (Print) | 0094-243X |

ISSN (Electronic) | 1551-7616 |

### Conference

Conference | 1st International Conference on Mathematical Sciences and Technology 2018: Innovative Technologies for Mathematics and Mathematics for Technological Innovation, MathTech 2018 |
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Country/Territory | Malaysia |

City | Penang |

Period | 10/12/18 → 12/12/18 |