Issue |
ESAIM: COCV
Volume 30, 2024
|
|
---|---|---|
Article Number | 61 | |
Number of page(s) | 30 | |
DOI | https://doi.org/10.1051/cocv/2024050 | |
Published online | 10 September 2024 |
Constrained mean-variance investment-reinsurance under the Cramér–Lundberg model with random coefficients
1
School of Statistics and Mathematics, Shandong University of Finance and Economics, Jinan 250100, PR China
2
Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, PR China
* Corresponding author: maxu@polyu.edu.hk
Received:
14
November
2023
Accepted:
14
June
2023
In this paper, we study an optimal mean-variance investment-reinsurance problem for an insurer (she) under the Cramér–Lundberg model with random coefficients. At any time, the insurer can purchase reinsurance or acquire new business and invest her surplus in a security market consisting of a risk-free asset and multiple risky assets, subject to a general convex cone investment constraint. We reduce the problem to a constrained stochastic linear-quadratic control problem with jumps whose solution is related to a system of partially coupled stochastic Riccati equations (SREs). Then we devote ourselves to establishing the existence and uniqueness of solutions to the SREs by pure backward stochastic differential equation (BSDE) techniques. We achieve this with the help of approximation procedure, comparison theorems for BSDEs with jumps, log transformation and BMO martingales. The efficient investment-reinsurance strategy and efficient mean-variance frontier are explicitly given through the solutions of the SREs, which are shown to be a linear feedback form of the wealth process and a half-line, respectively.
Mathematics Subject Classification: 93E20 / 60H30 / 91G10
Key words: Mean-variance investment-reinsurance / convex cone constraints / random coefficients / partially coupled stochastic Riccati equations / backward stochastic differential equations with jumps
© The authors. Published by EDP Sciences, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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