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Permutation Monotone Functions of Random Vectors with Applications in Financial and Actuarial Risk Management

Part of: Distribution theory - Probability Mathematical economics

Published online by Cambridge University Press:  04 January 2016

Xiaohu Li  and
Yinping You
Xiaohu Li*
Affiliation:
Stevens Institute of Technology
Yinping You*
Affiliation:
Huaqiao University
*
∗ Postal address: Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken, NJ 07030, USA. Email address: [email protected], [email protected]
∗∗ Postal address: School of Mathematical Sciences, Huaqiao University, Quanzhou, 362021, China.
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Abstract

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In this paper we develop two permutation theorems on argument increasing functions of a multivariate random vector and a real parameter vector. We use the unified approach of our two theorems to provide some important theoretical results on the capital allocation in actuarial science, the deductible and upper limit allocations in insurance policy, and portfolio allocation in financial engineering. Our results successfully improve or extend the corresponding works in the literature.

Keywords

Archimedean copulaarrangement increasingdeductibledistortion measurestochastic orderupper limitutility function

MSC classification

Primary: 91B16: Utility theory 91B30: Risk theory, insurance
Secondary: 60E15: Inequalities; stochastic orderings
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 47 , Issue 1 , March 2015 , pp. 270 - 291
Copyright
© Applied Probability Trust 

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