Capital Allocation Using the Bootstrap

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

This paper investigates the use of the bootstrap in capital allocation. In particular, for the distortion risk measure (DRM) class, we show that the exact bootstrap estimate is available in analytic form for the allocated capital. We then theoretically justify the bootstrap bias correction for the allocated capital induced from the concave DRM when the conditional mean function is strictly monotone. A numerical example shows a tradeoff exists between the bias reduction and variance increase in bootstrapping the allocated capital. However, unlike the aggregate capital case, the variance increase of the bias-corrected allocated capital estimate substantially outweighs the benefit of bias correction, making the bootstrap bias correction at the allocated capital level not as useful. Overall, the exact bootstrap without bias correction offers an efficient method for determining allocation over the ordinary resampling bootstrap estimate and the empirical counterpart.

Original languageEnglish
Pages (from-to)499-516
Number of pages18
JournalNorth American Actuarial Journal
Volume15
Issue number4
DOIs
Publication statusPublished - 2011 Oct 1

Fingerprint

Bootstrap
Bias Correction
Risk Measures
Estimate
Bias Reduction
Bootstrapping
Resampling
Justify
Capital allocation
Monotone
Strictly
Trade-offs
Numerical Examples
Bias correction
Distortion risk measure

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty

Cite this

@article{72f17508a1be4d028de831d23ba4fbb2,
title = "Capital Allocation Using the Bootstrap",
abstract = "This paper investigates the use of the bootstrap in capital allocation. In particular, for the distortion risk measure (DRM) class, we show that the exact bootstrap estimate is available in analytic form for the allocated capital. We then theoretically justify the bootstrap bias correction for the allocated capital induced from the concave DRM when the conditional mean function is strictly monotone. A numerical example shows a tradeoff exists between the bias reduction and variance increase in bootstrapping the allocated capital. However, unlike the aggregate capital case, the variance increase of the bias-corrected allocated capital estimate substantially outweighs the benefit of bias correction, making the bootstrap bias correction at the allocated capital level not as useful. Overall, the exact bootstrap without bias correction offers an efficient method for determining allocation over the ordinary resampling bootstrap estimate and the empirical counterpart.",
author = "Kim, {Joseph H.T.}",
year = "2011",
month = "10",
day = "1",
doi = "10.1080/10920277.2011.10597635",
language = "English",
volume = "15",
pages = "499--516",
journal = "North American Actuarial Journal",
issn = "1092-0277",
publisher = "Society of Actuaries",
number = "4",

}

Capital Allocation Using the Bootstrap. / Kim, Joseph H.T.

In: North American Actuarial Journal, Vol. 15, No. 4, 01.10.2011, p. 499-516.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Capital Allocation Using the Bootstrap

AU - Kim, Joseph H.T.

PY - 2011/10/1

Y1 - 2011/10/1

N2 - This paper investigates the use of the bootstrap in capital allocation. In particular, for the distortion risk measure (DRM) class, we show that the exact bootstrap estimate is available in analytic form for the allocated capital. We then theoretically justify the bootstrap bias correction for the allocated capital induced from the concave DRM when the conditional mean function is strictly monotone. A numerical example shows a tradeoff exists between the bias reduction and variance increase in bootstrapping the allocated capital. However, unlike the aggregate capital case, the variance increase of the bias-corrected allocated capital estimate substantially outweighs the benefit of bias correction, making the bootstrap bias correction at the allocated capital level not as useful. Overall, the exact bootstrap without bias correction offers an efficient method for determining allocation over the ordinary resampling bootstrap estimate and the empirical counterpart.

AB - This paper investigates the use of the bootstrap in capital allocation. In particular, for the distortion risk measure (DRM) class, we show that the exact bootstrap estimate is available in analytic form for the allocated capital. We then theoretically justify the bootstrap bias correction for the allocated capital induced from the concave DRM when the conditional mean function is strictly monotone. A numerical example shows a tradeoff exists between the bias reduction and variance increase in bootstrapping the allocated capital. However, unlike the aggregate capital case, the variance increase of the bias-corrected allocated capital estimate substantially outweighs the benefit of bias correction, making the bootstrap bias correction at the allocated capital level not as useful. Overall, the exact bootstrap without bias correction offers an efficient method for determining allocation over the ordinary resampling bootstrap estimate and the empirical counterpart.

UR - http://www.scopus.com/inward/record.url?scp=84862948595&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84862948595&partnerID=8YFLogxK

U2 - 10.1080/10920277.2011.10597635

DO - 10.1080/10920277.2011.10597635

M3 - Article

VL - 15

SP - 499

EP - 516

JO - North American Actuarial Journal

JF - North American Actuarial Journal

SN - 1092-0277

IS - 4

ER -