國立虎尾科技大學 |

Optimization Approaches in Risk Management.

紀錄類型:	書目-語言資料,手稿 : Monograph/item
正題名/作者:	Optimization Approaches in Risk Management./
作者:	Maritato, Kevin.
面頁冊數:	1 online resource (97 pages)
附註:	Source: Dissertations Abstracts International, Volume: 85-09, Section: A.
Contained By:	Dissertations Abstracts International85-09A.
標題:	Applied mathematics. -
電子資源:	click for full text (PQDT)
ISBN:	9798381949605

Optimization Approaches in Risk Management.
Maritato, Kevin.

Optimization Approaches in Risk Management. - 1 online resource (97 pages)

Source: Dissertations Abstracts International, Volume: 85-09, Section: A.

Thesis (Ph.D.)--State University of New York at Stony Brook, 2023.

Includes bibliographical references

The reduced cumulative distribution function (rCDF) is the maximal lower bound for the cumulative distribution function (CDF). It is equivalent to the inverse of the conditional value at risk (CVaR), or one minus the buffered probability of exceedance (bPOE). This dissertation introduces the reduced probability density function (rPDF), the derivative of rCDF. We first explore the relation between rCDF and other risk measures. Then we describe three means of calculating rPDF for a distribution, depending on what is known about the distribution. For functions with a closed-form formula for bPOE, we derive closed-form formulae for rPDF. Further, we describe formulae for rPDF based on a numerical bPOE when there is a closed-form formula for CVaR but no closed-form formula for bPOE. Finally, we give a method for numerically calculating rPDF for an empirical distribution, and compare the results with other methods for known distributions. We conducted two case studies, one using rPDF for sensitivity analysis and another using rPDF for parameter estimation with a method similar to the maximum likelihood method.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798381949605Subjects--Topical Terms:

1069907
Applied mathematics.
Subjects--Index Terms:

Sensitivity analysisIndex Terms--Genre/Form:

554714
Electronic books.

Optimization Approaches in Risk Management.
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500 $a Advisor: Uryasev, Stan;Polak, Pawel.
502 $a Thesis (Ph.D.)--State University of New York at Stony Brook, 2023.
504 $a Includes bibliographical references
520 $a The reduced cumulative distribution function (rCDF) is the maximal lower bound for the cumulative distribution function (CDF). It is equivalent to the inverse of the conditional value at risk (CVaR), or one minus the buffered probability of exceedance (bPOE). This dissertation introduces the reduced probability density function (rPDF), the derivative of rCDF. We first explore the relation between rCDF and other risk measures. Then we describe three means of calculating rPDF for a distribution, depending on what is known about the distribution. For functions with a closed-form formula for bPOE, we derive closed-form formulae for rPDF. Further, we describe formulae for rPDF based on a numerical bPOE when there is a closed-form formula for CVaR but no closed-form formula for bPOE. Finally, we give a method for numerically calculating rPDF for an empirical distribution, and compare the results with other methods for known distributions. We conducted two case studies, one using rPDF for sensitivity analysis and another using rPDF for parameter estimation with a method similar to the maximum likelihood method.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2024
538 $a Mode of access: World Wide Web
650 4 $a Applied mathematics. $3 1069907
650 4 $a Statistics. $3 556824
650 4 $a Finance. $3 559073
653 $a Sensitivity analysis
653 $a Buffered probability of exceedance
653 $a Cumulative distribution function
653 $a Closed-form formula
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710 2 $a State University of New York at Stony Brook. $b Applied Mathematics and Statistics. $3 1179106
773 0 $t Dissertations Abstracts International $g 85-09A.
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