Optimal Reinsurance to Minimize the Probability of Drawdown under the Mean-Variance Premium Principle: Asymptotic Analysis
In this paper, we consider an optimal reinsurance problem to minimize the probability of drawdown for the scaled Cram´er-Lundberg risk model when the reinsurance premium is computed according to the mean-variance premium principle. We extend the work of Liang et al. [16] to the case of minimizing...
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SIAM Journal on Financial Mathematics
2023
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| Acceso en línea: | https://repositorio.utdt.edu/handle/20.500.13098/11875 https://doi.org/10.1137/21M1461666 |
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I57-R163-20.500.13098-118752023-07-28T14:40:31Z Optimal Reinsurance to Minimize the Probability of Drawdown under the Mean-Variance Premium Principle: Asymptotic Analysis Azcue, Pablo Muler, Nora Liang, Xiaoqing Young, Virginia R. Optimal reinsurance Probability of drawdown Scaled Cram´er-Lundbergmodel Asymptotic analysis Diffusion approximation In this paper, we consider an optimal reinsurance problem to minimize the probability of drawdown for the scaled Cram´er-Lundberg risk model when the reinsurance premium is computed according to the mean-variance premium principle. We extend the work of Liang et al. [16] to the case of minimizing the probability of drawdown. By using the comparison method and the tool of adjustment coefficients, we show that the minimum probability of drawdown for the scaled classical risk model converges to the minimum probability for its diffusion approximation, and the rate of convergence is of order O(n−1/2). We further show that using the optimal strategy from the diffusion approximation in the scaled classical risk model is O(n−1/2)-optimal Este documento es una versión del artículo publicado en SIAM Journal on Financial Mathematics, 14(1), 279–313 Universidad Torcuato Di Tella Hebei University of Technology Department of Mathematics, University of Michigan 2023-06-14T20:40:28Z 2023-06-14T20:40:28Z 2023 info:eu-repo/semantics/article info:eu-repo/semantics/submittedVersion https://repositorio.utdt.edu/handle/20.500.13098/11875 https://doi.org/10.1137/21M1461666 eng Azcue, P., Liang, X., Muler, N., & Young, V. R. (2023). Optimal Reinsurance to Minimize the Probability of Drawdown under the Mean-Variance Premium Principle: Asymptotic Analysis. SIAM Journal on Financial Mathematics, 14(1), 279–313. https://doi.org/10.1137/21m1461666 info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-sa/2.5/ar/ 37 p. application/pdf application/pdf SIAM Journal on Financial Mathematics |
| institution |
Universidad Torcuato Di Tella |
| institution_str |
I-57 |
| repository_str |
R-163 |
| collection |
Repositorio Digital Universidad Torcuato Di Tella |
| language |
Inglés |
| orig_language_str_mv |
eng |
| topic |
Optimal reinsurance Probability of drawdown Scaled Cram´er-Lundbergmodel Asymptotic analysis Diffusion approximation |
| spellingShingle |
Optimal reinsurance Probability of drawdown Scaled Cram´er-Lundbergmodel Asymptotic analysis Diffusion approximation Azcue, Pablo Muler, Nora Liang, Xiaoqing Young, Virginia R. Optimal Reinsurance to Minimize the Probability of Drawdown under the Mean-Variance Premium Principle: Asymptotic Analysis |
| topic_facet |
Optimal reinsurance Probability of drawdown Scaled Cram´er-Lundbergmodel Asymptotic analysis Diffusion approximation |
| description |
In this paper, we consider an optimal reinsurance problem to minimize the probability of drawdown
for the scaled Cram´er-Lundberg risk model when the reinsurance premium is computed
according to the mean-variance premium principle. We extend the work of Liang et al. [16] to
the case of minimizing the probability of drawdown. By using the comparison method and the
tool of adjustment coefficients, we show that the minimum probability of drawdown for the scaled
classical risk model converges to the minimum probability for its diffusion approximation, and the
rate of convergence is of order O(n−1/2). We further show that using the optimal strategy from
the diffusion approximation in the scaled classical risk model is O(n−1/2)-optimal |
| format |
Artículo submittedVersion |
| author |
Azcue, Pablo Muler, Nora Liang, Xiaoqing Young, Virginia R. |
| author_facet |
Azcue, Pablo Muler, Nora Liang, Xiaoqing Young, Virginia R. |
| author_sort |
Azcue, Pablo |
| title |
Optimal Reinsurance to Minimize the Probability of Drawdown under the Mean-Variance Premium Principle: Asymptotic Analysis |
| title_short |
Optimal Reinsurance to Minimize the Probability of Drawdown under the Mean-Variance Premium Principle: Asymptotic Analysis |
| title_full |
Optimal Reinsurance to Minimize the Probability of Drawdown under the Mean-Variance Premium Principle: Asymptotic Analysis |
| title_fullStr |
Optimal Reinsurance to Minimize the Probability of Drawdown under the Mean-Variance Premium Principle: Asymptotic Analysis |
| title_full_unstemmed |
Optimal Reinsurance to Minimize the Probability of Drawdown under the Mean-Variance Premium Principle: Asymptotic Analysis |
| title_sort |
optimal reinsurance to minimize the probability of drawdown under the mean-variance premium principle: asymptotic analysis |
| publisher |
SIAM Journal on Financial Mathematics |
| publishDate |
2023 |
| url |
https://repositorio.utdt.edu/handle/20.500.13098/11875 https://doi.org/10.1137/21M1461666 |
| work_keys_str_mv |
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1808040594845466624 |