Some new notions of dependence with applications in optimal allocation problems |
| |
| Affiliation: | 1. Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1;2. Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI, 53211, USA;1. Netspar, CentER, Department of Econometrics and Operations Research, Tilburg University, Netherlands;2. APG and Netspar, CentER, Department of Economics, Tilburg University, Netherlands;3. Netspar, Faculty of Economics and Business, University of Amsterdam, Netherlands;1. University of Oslo, Norway;2. University of Barcelona, Spain;1. School of Hydropower & Information Engineering, Huazhong University of Science and Technology, Wuhan 430074, China;2. Beijing Engineering Corporation Limited, Beijing 100024, China;3. College of Renewable Energy, North China Electric Power University, Beijing 102206, China;1. Department of Statistics, Ewha Womans University, Seoul, Republic of Korea;2. Department of Statistics and Actuarial Science, Simon Fraser University, BC, Canada;3. Department of Mathematics and Statistics, Concordia University, Montreal, QC, Canada |
| |
| Abstract: | Dependence structures of multiple risks play an important role in optimal allocation problems for insurance, quantitative risk management, and finance. However, in many existing studies on these problems, risks or losses are often assumed to be independent or comonotonic or exchangeable. In this paper, we propose several new notions of dependence to model dependent risks and give their characterizations through the probability measures or distributions of the risks or through the expectations of the transformed risks. These characterizations are related to the properties of arrangement increasing functions and the proposed notions of dependence incorporate many typical dependence structures studied in the literature for optimal allocation problems. We also develop the properties of these dependence structures. We illustrate the applications of these notions in the optimal allocation problems of deductibles and policy limits and in capital reserves problems. These applications extend many existing researches to more general dependent risks. |
| |
| Keywords: | Dependence notion Arrangement increasing Stochastic order SAI RWSAI CUOAI UOAI Comonotonicity Copula Optimal allocation Deductible Policy limit Capital reserve |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
