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The time of deducting fees for variable annuities under the state-dependent fee structure |
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| Affiliation: | 1. School of Mathematical Sciences, Peking University, Beijing 100871, PR China;2. Key Laboratory of Mathematical Economics and Quantitative Finance, Peking University, Beijing 100871, PR China;1. Department of Mathematics, University of Zagreb, Bijenička 30, Zagreb, Croatia;2. Faculty of Mining, Geology and Petroleum Engineering, University of Zagreb, Pierottijeva 6, Zagreb, Croatia;1. Department of Finance, National Chung Cheng University, Minhsiung, 621, Taiwan;2. Risk and Insurance Research Center, National Chengchi University, Taipei, Taiwan;3. Department of Statistics and Actuarial Science, Simon Fraser University, Burnaby, BC V5A 1S6, Canada;1. Department of Statistical Sciences, University of Toronto, Toronto, Ontario M5S 3G3, Canada;2. Quantitative Engineering and Development, TD Securities, Toronto, Ontario M5K 1A2, Canada;3. Department of Statistics and Actuarial Science, University of Iowa, Iowa City, IA 52242, USA |
| Abstract: | We investigate the total time of deducting fees for variable annuities with state-dependent fee. This fee charging method is studied recently by Bernard et al. (2014) and Delong (2014) in which the fees deducted from the policyholder’s account depend on the account value. However, both of them have not considered the problem of analyzing probabilistic properties of the total time of deducting fees. We approximate the maturity of a general variable annuity contract by combinations of exponential distributions which are (weakly) dense in the space that is composed of all probability distributions on the positive axis. Working under general jump diffusion process, we derive analytic formulas for the expectation of the time of deducting fees as well as its Laplace transform. |
| Keywords: | Variable annuities State-dependent fee Hyper-exponential jump diffusion process Laplace transform Refracted Lévy process |
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