Dynamic Monitoring and Forecasting of the Soundness of U.S. Insurers in a Cyclical Environment

Hong Mao; Wei Hao

doi:10.1515/apjri-2018-0006

Article

Dynamic Monitoring and Forecasting of the Soundness of U.S. Insurers in a Cyclical Environment

Hong Mao and Wei Hao

Published/Copyright: January 12, 2019

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From the journal Asia-Pacific Journal of Risk and Insurance Volume 13 Issue 1

Abstract

This paper presents a model of dynamic monitoring and forecasting of key financial indices of U.S. insurers. The key financial indices are assumed to be cyclically time-varying correlated and are selected according to their impact on the soundness of the insurers. It also presents a new kind of control chart, μr chart, based on the weighted average of standardized financial indices. Three kinds of objective functions are applied to determine the optimal weights: (1) minimizing the probability of a missed alarm; (2) minimizing the volatility of the weighted average of standardized financial indices; and (3) minimizing the expected shortfall of the weighted average of standardized financial indices. We note that the optimal weights are equal weights no matter which objective function is selected. The control technique presented in this paper can be extended to monitor the soundness of other insurance firms in a cyclical environment.

Keywords: unified approach; dynamic monitoring; forecasting; µr(t) chart; cyclical environment; important financial indices

Appendix

We calculate the time-dependent covariance of σij(t) of the return of stocks and bonds in a manner similar to Korn and Koziol (2006) as well as Mamon (2004).

Vasicek model: dr=ab−rdt+σdWuWrite Xu=ru−bdXt=−aXt+ σdWtXu=e−auX0+∫0uσeasdws

In the following, we calculate the time-varying covariance, σij(t), By Itô isometry, we have:

σij(t)=Covrit(t),rjt(t)=E(rit(t)rjt(t))−Erit(t)Erjt(t)=Ebi+(ri0−bi)e−ait+σie−ait∫0teaisdwsbj+(rj0−bj)e−ajt+σje−ajt∫0teajsdws−bi+(ri0−bi)e−aitbj+(rj0−bj)e−ajt=σiσje−ait−ajtE(∫0teaisdws∫0teajsdws)=σiσje−ait−ajt∫0te(ai+aj)sds=σiσjai+aj1−e−(ai+aj)t.

Please note that σi2(t)=σij(t); when i=j, σi2(t)=σi22ai1−e−2ait.

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Published Online: 2019-01-12

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Articles in the same Issue

https://doi.org/10.1515/apjri-2018-0006

Keywords for this article

unified approach; dynamic monitoring; forecasting; µr(t) chart; cyclical environment; important financial indices