Ordering optimal deductible allocations for stochastic arrangement increasing risks |
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| Affiliation: | 1. School of Science, Tianjin University of Commerce, Tianjin 300134, China;2. Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken NJ 07030, USA;1. Department of Statistics and Actuarial Science, University of Waterloo, Canada;2. Department of Mathematics and Statistics, University of Bern, Switzerland;1. School of Economics and Management, University of Firenze, Italy;2. Department of Mathematical Stochastics, University of Freiburg, Freiburg, Germany;1. Cass Business School, City, University of London, United Kingdom;2. DEAMS, University of Trieste, Italy |
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| Abstract: | The insurer usually solicits the insured through granting a certain amount of deductible to multiple risks according to his/her own will. Due to the nonlinear nature of the concerned optimization problem, in the literature on the optimal allocations of deductibles researchers usually assume independence or comonotonicity among concerned risks and ignore the impact due to frequency. In this study we build two sufficient conditions for the decreasing optimal allocation of deductibles, relaxing the stochastic arrangement increasing or right tail weakly stochastic arrangement increasing discount factors in Cai and Wei (2014, Theorems 6.3 and 6.6) to the conditionally upper orthant arrangement increasing or weak conditionally upper orthant arrangement increasing frequencies. |
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| Keywords: | Comonotone Conditionally upper orthant arrangement increasing Occurrence frequency Stochastic order Mean residual lifetime order |
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