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Ordering scalar products with applications in financial engineering and actuarial science

Published online by Cambridge University Press:  24 March 2016

Yinping You  and
Xiaohu Li
Yinping You
Affiliation:
School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian, 362021, China.
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Abstract

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In this paper we build the increasing convex (concave) order for the scalar product of random vectors with an upper (lower) tail permutation decreasing joint density. As applications, we revisit allocations of portfolio risks in financial engineering and of coverage limits and deductibles in insurance. Some related results in the literature are substantially updated.

Keywords

Archimedean copulacoverage limitdeductiblemajorizationupper tail permutation decreasing
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 1 , March 2016 , pp. 47 - 56
Copyright
Copyright © Applied Probability Trust 2016 

References

Cai, J. and Wei, W. (2014). Some new notions of dependence with applications in optimal allocation problems. Insurance Math. Econom. 55, 200–209. CrossRefGoogle Scholar
Cai, J. and Wei, W. (2015). Notions of multivariate dependence and their applications in optimal portfolio selections with dependent risks. J. Multivariate Anal. 138, 156–169. Google Scholar
Chen, Z. and Hu, T. (2008). Asset proportions in optimal portfolios with dependent default risks. Insurance Math. Econom. 43, 223–226. Google Scholar
Cheung, K. C. (2006). Optimal portfolio problem with unknown dependency structure. Insurance Math. Econom. 38, 167–175. Google Scholar
Cheung, K. C. and Yang, H. (2004). Ordering optimal proportions in the asset allocation problem with dependent default risks. Insurance Math. Econom. 35, 595–609. Google Scholar
Denuit, M., Dhaene, J., Goovaerts, M. and Kaas, R. (2005). Actuarial Theory for Dependent Risks. John Wiley, Hoboken, NJ. CrossRefGoogle Scholar
Hennessy, D. A. and Lapan, H. E. (2002). The use of Archimedean copulas to model portfolio allocations. Math. Finance 12, 143–154. CrossRefGoogle Scholar
Hua, L. and Cheung, K. C. (2008). Stochastic orders of scalar products with applications. Insurance Math. Econom. 42, 865–872. CrossRefGoogle Scholar
Li, X. and You, Y. (2012). On allocation of upper limits and deductibles with dependent frequencies and comonotonic severities. Insurance Math. Econom. 50, 423–429. Google Scholar
Li, X. and You, Y. (2014). A note on allocation of portfolio shares of random assets with Archimedean copul. Ann. Operat. Res. 212, 155–167. CrossRefGoogle Scholar
Li, X. and You, Y. (2015). Permutation monotone functions of random vectors with applications in financial and actuarial risk management. Adv. Appl. Prob. 47, 270–291. CrossRefGoogle Scholar
Ma, C. (2000). Convex orders for linear combinations of random variables. J. Statist. Planning Infer. 84, 11–25. Google Scholar
Marshall, A. W., Olkin, I. and Arnold, B. C. (2011). Inequalities: Theory of Majorization and Its Applications, 2nd edn. Springer, New York. Google Scholar
You, Y. and Li, X. (2014). Optimal capital allocations to interdependent actuarial risks. Insurance Math. Econom. 57, 104–113. Google Scholar
You, Y. and Li, X. (2015). Most unfavorable deductibles and coverage limits for multiple random risks with Archimedean copulas. To appear in Ann. Operat. Res.Google Scholar
Zhuang, W., Chen, Z. and Hu, T. (2009). Optimal allocation of policy limits and deductibles under distortion risk measures. Insurance Math. Econom. 44, 409–414. CrossRefGoogle Scholar