In this paper, we consider the robust investment and reinsurance problem with bounded memory and risk co-shocks under a jump-diffusion risk model. The insurer is assumed to be ambiguity-averse and make the optimal decision under the mean-variance criterion. The insurance market is described by two-dimensional dependent claims while the risky asset is depicted by the jump-diffusion model. By introducing the performance in the past, we derive the wealth process depicted by a stochastic delay differential equation (SDDE). Applying the stochastic control theory under the game-theoretic framework, together with stochastic control theory with delay, the robust equilibrium investment-reinsurance strategy and the corresponding robust equilibrium value function are derived. Furthermore, some numerical examples are provided to illustrate the effect of market parameters on the optimal investment and reinsurance strategy.
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DOI : 10.1051/ro/2021182
Keywords: Robust investment and reinsurance, mean-variance, jump-diffusion, two-dimensional claim, game theory
@article{RO_2022__56_1_77_0,
author = {Li, Sheng},
title = {Robust equilibrium investment and reinsurance strategy with bounded memory and common shock dependence},
journal = {RAIRO. Operations Research},
pages = {77--99},
year = {2022},
publisher = {EDP-Sciences},
volume = {56},
number = {1},
doi = {10.1051/ro/2021182},
mrnumber = {4376287},
zbl = {1482.91185},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2021182/}
}
TY - JOUR AU - Li, Sheng TI - Robust equilibrium investment and reinsurance strategy with bounded memory and common shock dependence JO - RAIRO. Operations Research PY - 2022 SP - 77 EP - 99 VL - 56 IS - 1 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ro/2021182/ DO - 10.1051/ro/2021182 LA - en ID - RO_2022__56_1_77_0 ER -
%0 Journal Article %A Li, Sheng %T Robust equilibrium investment and reinsurance strategy with bounded memory and common shock dependence %J RAIRO. Operations Research %D 2022 %P 77-99 %V 56 %N 1 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ro/2021182/ %R 10.1051/ro/2021182 %G en %F RO_2022__56_1_77_0
Li, Sheng. Robust equilibrium investment and reinsurance strategy with bounded memory and common shock dependence. RAIRO. Operations Research, Tome 56 (2022) no. 1, pp. 77-99. doi: 10.1051/ro/2021182
[1] , and , A quartet of semigroups for model specification, robustness, prices of risk, and model detection. J. Eur. Econ. Assoc. 1 (2003) 68–123. | DOI
[2] and , Optimal proportional reinsurance and investment with multiple risky assets and no-shorting constraint. Insurance Math. Econ. 42 (2008) 968–975. | MR | Zbl | DOI
[3] and , Dynamic mean-variance problem with constrained risk control for the insurers. Math. Methods Oper. Res. 68 (2008) 181–205. | MR | Zbl | DOI
[4] , Benchmark and mean-variance problems for insurers. Math. Methods Oper. Res. 62 (2005) 159–165. | MR | Zbl | DOI
[5] and , Optimal mean-variance problem with constrained controls in a jump-diffusion financial market for an insurer. J. Optim. Theory App. 157 (2013) 252–275. | MR | Zbl | DOI
[6] and , A general theory of markovian time inconsistent stochastic control problems. Working paper, Stockholm School of School (2010).
[7] , and , On time-inconsistent stochastic control in continuous time. Finance Stochastics 21 (2017) 331–360. | MR | Zbl | DOI
[8] and , Robust portfolio choice with uncertainty about jump and diffusion risk. J. Banking Finance 37 (2013) 5036–5047. | DOI
[9] , Optimal investment policies for a firm with a random risk process: exponential utility and minimizing the probability of ruin. Math. Oper. Res. 20 (1995) 937–958. | MR | Zbl | DOI
[10] and , Optimal proportional reinsurance and investment based on Hamilton–Jacobi–Bellman equation. Insurance Math. Econ. 45 (2009) 157–162. | MR | Zbl | DOI
[11] , and , A stochastic portfolio optimization model with bounded memory. Math. Oper. Res. 36 (2011) 604–619. | MR | Zbl | DOI
[12] and , Robust optimal reinsurance-investment strategy with price jumps and correlated claims. Insurance Math. Econ. 92 (2020) 27–46. | MR | Zbl | DOI
[13] , Aspects of Risk Theory. Springer-Verlag, New York (1991). | MR | Zbl | DOI
[14] and , Optimal investment for insurers. Insurance Math. Econ. 27 (2000) 215–228. | MR | Zbl | DOI
[15] and , Optimal proportional reinsurance policies for diffusion models with transaction costs. Special issue on the interplay between insurance, finance and control. Insurance Math. Econ. 22 (1998) 41–51. | MR | Zbl | DOI
[16] and , Optimal dynamic portfolio selection: multiperiod mean-variance formulation. Math. Finance 10 (2000) 387–406. | MR | Zbl | DOI
[17] and , Time-consistent mean-variance reinsurance-investment strategy for insurers under CEV model. Scand. Actuarial J. 2016 (2016) 646–671. | MR | Zbl | DOI
[18] , Robust portfolio rules and detection-error probabilities for a mean-reverting risk premium. J. Econ. Theory 128 (2006) 136–163. | MR | Zbl | DOI
[19] , Portfolio selection. J. Finance 7 (1952) 77–91.
[20] and , A maximum principle for optimal control of stochastic systems with delay, with applications to finance. In: Optimal Control and Partial Differential Equations-Innovations and Applications, edited by , and . IOS Press, Amsterdam, The Netherlands (2000) 64–79. | MR | Zbl
[21] , Stochastic Control in Insurance. Springer-Verlag, London, (2008). | MR | Zbl
[22] and , Optimal investment-reinsurance with delay for mean-variance insurers: a maximum principle approach. Insurance Math. Econ. 57 (2014) 1–12. | MR | Zbl | DOI
[23] , and , Maximum principle for mean-field jump-diffusion stochastic delay differential equations and its application to finance. Automatica 50 (2014) 1565–1579. | MR | Zbl | DOI
[24] and , Optimal investment for insurer with jump-diffusion risk process. Insurance Math. Econ. 37 (2005) 615–634. | MR | Zbl | DOI
[25] , , and , Robust optimal strategies for an insurer with reinsurance and investment under benchmark and mean-variance criteria. Scand. Actuarial J. 2015 (2015) 725–751. | MR | Zbl | DOI
[26] and , Optimal time-consistent investment and reinsurance policies for mean-variance insurers. Insurance Math. Econ. 49 (2011) 145–154. | MR | Zbl | DOI
[27] , and , Time-consistent investment and reinsurance strategies for mean-variance insurers with jumps. Insurance Math. Econ. 52 (2013) 498–507. | MR | Zbl | DOI
[28] , and , Robust equilibrium reinsurance-investment strategy for a mean-variance insurer in a model with jumps. Insurance Math. Econ. 66 (2016) 138–152. | MR | Zbl | DOI
[29] and , Continuous-time mean-variance portfolio selection: a stochastic LQ framework. Appl. Math. Optim. 42 (2000) 19–33. | MR | Zbl | DOI
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