This paper considers the optimal investment-reinsurance problem under the monotone mean-variance preference. The monotone mean-variance preference is a monotone version of the classical mean-variance preference. First of all, we reformulate the original problem as a zero-sum stochastic differential game. Secondly, the optimal strategy and the optimal value function for the monotone mean-variance problem are derived by the approach of dynamic programming and the Hamilton-Jacobi-Bellman-Isaacs equation. Thirdly, the efficient frontier is obtained and it is proved that the optimal strategy is an efficient strategy. Finally, the continuous-time monotone capital asset pricing model is derived.
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DOI : 10.1051/ro/2021114
Keywords: Optimal reinsurance, Monotone mean-variance preference, Hamilton-Jacobi-Bellman-Isaacs equation, Monotone, efficient frontier, Capital asset pricing model
@article{RO_2021__55_4_2469_0,
author = {Li, Bohan and Guo, Junyi},
title = {Optimal reinsurance and investment strategies for an insurer under monotone mean-variance criterion},
journal = {RAIRO. Operations Research},
pages = {2469--2489},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {4},
doi = {10.1051/ro/2021114},
mrnumber = {4303673},
zbl = {1471.91468},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2021114/}
}
TY - JOUR AU - Li, Bohan AU - Guo, Junyi TI - Optimal reinsurance and investment strategies for an insurer under monotone mean-variance criterion JO - RAIRO. Operations Research PY - 2021 SP - 2469 EP - 2489 VL - 55 IS - 4 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ro/2021114/ DO - 10.1051/ro/2021114 LA - en ID - RO_2021__55_4_2469_0 ER -
%0 Journal Article %A Li, Bohan %A Guo, Junyi %T Optimal reinsurance and investment strategies for an insurer under monotone mean-variance criterion %J RAIRO. Operations Research %D 2021 %P 2469-2489 %V 55 %N 4 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ro/2021114/ %R 10.1051/ro/2021114 %G en %F RO_2021__55_4_2469_0
Li, Bohan; Guo, Junyi. Optimal reinsurance and investment strategies for an insurer under monotone mean-variance criterion. RAIRO. Operations Research, Tome 55 (2021) no. 4, pp. 2469-2489. doi: 10.1051/ro/2021114
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