Time-Consistent Investment and Reinsurance Strategies for Mean-Variance Insurers under Stochastic Interest Rate and Stochastic Volatility

Zhu, Jiaqi; Li, Shenghong

doi:10.3390/math8122183

Cited by 8 publications

(5 citation statements)

References 33 publications

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“…Huang et al [21] considered the estimation of ruin probability in an insurance risk model with stochastic premium income. Zhu and Li [22] studied the time-consistent optimal investment and reinsurance problem for mean-variance insurers when considering both stochastic interest rate and stochastic volatility in the financial market. Furthermore, in order to attract more people to participate in the insurance business and achieve a win-win situation for the policyholder and the insurer, an insurance company has launched dividend insurance products.…”

Section: Literature Reviewmentioning

confidence: 99%

Numerical Method for a Perturbed Risk Model with Proportional Investment

2022

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In this paper, we study the perturbed risk model with a threshold dividend strategy and proportional investment. The insurance companies are allowed to invest their surplus in a financial market consisting of a risk-free asset and a risky asset in fixed proportions; the risky assets are modeled by the jump-diffusion process. Firstly, using the theory of the stochastic process and stochastic analysis, we obtained the integro-differential equations satisfied by the expected discounted dividend payments and the discounted penalty function. Secondly, we obtained the numerical approximate solutions of the integro-differential equations through the sinc method, since the analytical solutions of them are not easy to obtain, and we found that the error is within a manageable range. Finally, we considered some numerical examples where the claim sizes follow an exponential distribution, a mixture of two exponential distributions or the lognormal distribution in detail, and explored how perturbations and proportional investment affect dividends and ruin probability. Moreover, sensitive analysis showed that the proportion of the risky investment, the diffusion coefficient, the distribution of the claims and the positive jump in the risky assets investment all have explicit impacts on dividends and ruin probability.

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Section: Literature Reviewmentioning

confidence: 99%

Numerical Method for a Perturbed Risk Model with Proportional Investment

2022

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“…Rami et al [3] introduced the generalized (differential) Riccati equation, a new type of differential Riccati equation to both solve the algebraic equality/inequality constraints and matrix pseudoinverse, and to also prove that the solution to such an equation can identify all optimal controls. In recent years, some achievements have been made in applying the stochastic models: Zhu and Li [4] studied relevant questions by modeling interest rates in the market using the Vasicek model. They derived equilibrium reinsurance-investment strategies and value functions using a comprehensive dynamic programming approach.…”

Section: Introductionmentioning

confidence: 99%

Optimal Reinsurance–Investment Strategy Based on Stochastic Volatility and the Stochastic Interest Rate Model

Bei

Wang

et al. 2023

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This paper studies insurance companies’ optimal reinsurance–investment strategy under the stochastic interest rate and stochastic volatility model, taking the HARA utility function as the optimal criterion. It uses arithmetic Brownian motion as a diffusion approximation of the insurer’s surplus process and the variance premium principle to calculate premiums. In this paper, we assume that insurance companies can invest in risk-free assets, risky assets, and zero-coupon bonds, where the Cox–Ingersoll–Ross model describes the dynamic change in stochastic interest rates and the Heston model describes the price process of risky assets. The analytic solution of the optimal reinsurance–investment strategy is deduced by employing related methods from the stochastic optimal control theory, the stochastic analysis theory, and the dynamic programming principle. Finally, the influence of model parameters on the optimal reinsurance–investment strategy is illustrated using numerical examples.

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“…As per figure 1.2* below. The investment return for the insurance and reinsurance companies plays an important role in the company's profitability (Ab Rahim et al, 2021) The objective of this study is to help the insurance and reinsurance companies to construct the optimal investment allocation that will generate the required/adequate risk-adjusted return without affecting the overall financial performance of the insurance and reinsurance companies during the low-interest-rate environment (Zhu & Li, 2020).…”

Section: Introductionmentioning

confidence: 99%

The Optimal Investment Portfolio Management for Insurance and Reinsurance Companies in Gulf Cooperation Council (GCC)

Ahmed

2022

icebas

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This study aims to find the optimal investment portfolio management for the insurance and reinsurance companies in GCC. The researcher collected the data from the annual reports of the 30 companies listed in the respective stocks exchange from 2016 to 2020, based on the top five company's GWP from each GCC country as of 2020. Descriptive analysis for each country and each year of the study period was used to find the mean ROI and the average level of the strategic asset allocation; the pairwise correlation was used between the ROI and Libor. The results indicate the mean ROI for the insurance and reinsurance companies, the average level of SAA allocation by country and by year, the investment income has enormous effects on the performance of the insurance and reinsurance companies, the investment allocation to risky assets does not necessarily generate a high ROI, the thirty sampled insurance and reinsurance companies have generated ROI above 3%. This study contributes to the foundation of the investment portfolio management studies for insurance and reinsurance companies in the GCC countries.

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Time-Consistent Investment and Reinsurance Strategies for Mean-Variance Insurers under Stochastic Interest Rate and Stochastic Volatility

Cited by 8 publications

References 33 publications

Numerical Method for a Perturbed Risk Model with Proportional Investment

Numerical Method for a Perturbed Risk Model with Proportional Investment

Optimal Reinsurance–Investment Strategy Based on Stochastic Volatility and the Stochastic Interest Rate Model

The Optimal Investment Portfolio Management for Insurance and Reinsurance Companies in Gulf Cooperation Council (GCC)

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