【作者】 杨阳；

【导师】 王过京； 姚经；

【作者基本信息】 苏州大学 ， 金融工程， 2025， 博士

【摘要】 当下全球经济波动剧烈、金融市场复杂性上升,由此导致系统性风险不断累积,经济下行压力增大。面对这一严峻形势,党和政府明确提出“以强监管、防风险、促高质量发展为主线,充分发挥保险业的经济减震器和社会稳定器功能”,并着重强调要牢牢守住不发生系统性金融风险的底线。保险公司的核心职能是利用保费收入进行科学投资与提供专业的风险管理,当前复杂的经济环境与强监管的时代要求,对这两项职能的履行提出了更高的标准,因此,加强针对保险公司投资决策与风险管理的理论指导显得尤为迫切。本文从单一保险公司视角、多保险公司博弈视角、现实监管需求以及高阶风险的管理视角出发,系统研究保险公司的投资决策与风险管理,旨在为保险行业提供一套行之有效的理论与实践参考。首先,本文探讨了单一保险公司在基准偏离约束条件下的最优收益选择问题。通过引入Bregman-Wasserstein散度,构建了一种非对称偏离惩罚机制,能够实现对投资组合收益相对基准正负偏离的差异化调节,以此反映保险公司对损失与收益的非对称偏好。在理论层面,首次将Bregman-Wasserstein散度族融入基于期望效用的投资选择框架,技术上通过将原问题转化为泛函空间上的凸优化问题,证明了最优收益解的存在性和唯一性。此外,本文提出了带阈值的Bregman散度,该散度可以更精准地聚焦保险公司投资组合相对基准组合损失的部分,以便进行下行风险管理。数值分析结果表明,相比传统的对称约束方法,Bregman-Wasserstein散度在平衡收益增强与风险约束方面具有更高的灵活性,为投资组合优化与保险设计提供了一个全新的理论范式。其次,在保险公司的博弈视角下,本文研究了多家均值-方差保险公司在有错误定价和违约风险市场中的非零和随机微分博弈。该设定中,保险公司不仅可以购买比例再保险,还可以投资于无风险资产、市场指数、可违约债券以及多对错误定价股票。这些错误定价股票遵循“协整系统”,其预期收益服从均值回复过程,而债券则存在违约风险。特别地,本文假设仅少数保险公司可以投资错误定价股票,这更加符合现实情形,同时反映出了竞争市场中投资信息带来的优势。每家保险公司的目标是在均值-方差标准下,最大化自身的相对表现财富。利用随机控制理论,建立了扩展的哈密顿-雅可比-贝尔曼(HJB)方程,并成功获得了解析的均衡策略。进一步,验证了保险公司从错误定价股票投资机会中获得的竞争优势。有别于现有文献,本文采用M-矩阵展示结果,这不仅有助于证明解的存在性与唯一性,还能够简便地进行参数敏感性分析。再次,依据对保险业的现实监管要求,考虑了保险公司的最优资本配置问题,并提出一种新的广义尾均值-方差模型。该模型使用Bregman散度构造风险与资本间的距离函数,可以同时兼顾损失的大小和波动。本文不仅证明了最优资本配置的存在性和唯一性,而且提供了最优解满足的一般方程系统。进一步,引入了马氏尾均值-方差模型,推导出了不依赖分布的显式最优配置公式。应用上,选用多元广义双曲分布建模风险,推导了参数化的解析解;而对多元对数广义双曲分布的非负风险,则采用凸界近似方法获得了显式近似解。此外,通过两个数值实例,即标准普尔500行业部门指数的市场风险分析以及澳大利亚保险索赔数据的评估,展示了所提出的资本配置方法的有效性、稳健性和准确性。最后,立足高阶风险管理角度,探索了加权风险聚合模型下的两个新型风险度量:尾部矩(TM)和尾部联合矩(TJM)。这两个度量包含众多经典风险度量,并能量化如尾部偏度和尾部峰度的高阶矩风险。考虑到金融、保险数据通常具有非对称性和重尾性,本文采用多变量广义双曲分布建模风险。在此框架下,推导出了TM和TJM的解析表达式,为投资组合尾部风险的评估以及风险资产之间尾部相关性的分析提供便利。此外,通过两个实证案例展示了 TM和TJM在风险管理和投资组合选择中的优势及稳健性。第一个案例中,通过尾部条件偏度(TCS)和尾部条件峰度(TCK)评估资产尾分布构形与极端损失风险。第二个案例则关注下行市场中的风险依赖性,运用尾部相关性(TCOR)和尾部共偏度(TCOS)分析市场下跌期间股票与市场指数的风险相依,为对冲下行市场风险提供了重要参考。更多还原

【Abstract】 At present,the global economy is experiencing violent fluctuations and the complexity of financial markets is increasing,resulting in the accumulation of systemic risks and increasing downward pressure on the economy.In the face of this grim situation,the Party and the government have clearly proposed to "strengthen supervision,prevent risks and promote high-quality development as the main line,give full play to the functions of the insurance industry as an economic shock absorber and social stabilizer",and emphasize the need to firmly guard the bottom line of no systemic financial risks.The core function of insurance companies is to use premium income to make scientific investment and provide professional risk management.The current complex economic environment and the era of strong supervision require higher standards for the performance of these two functions.Therefore,it is particularly urgent to strengthen the theoretical guidance for insurance companies’ investment decision-making and risk management.This paper systematically studies the investment decision and risk management of insurance companies from the perspective of single insurance company,multi-insurance company game,realistic regulatory requirements and high-order risk management,aiming to provide a set of effective theoretical and practical reference for the insurance industry.First,we explore the problem of optimal revenue selection for a single insurer subject to a benchmark deviation constraint.By introducing Bregman-Wasserstein divergence,this paper constructs an asymmetric deviation penalty mechanism,which can realize the differential adjustment of positive deviation and negative deviation of portfolio returns.At the theoretical level,the Bregman-Wasserstein divergence family is integrated into the investment choice framework based on expected utility for the first time.In addition,this paper proposes the Bregman divergence with threshold,which can focus more precisely on the loss part of the insurance company’s portfolio relative to the benchmark portfolio for downside risk management.The numerical results show that the Bregman-Wasserstein divergence has higher flexibility in balancing return enhancement and risk constraints than the traditional symmetric constraint method,which provides a new theoretical paradigm for portfolio optimization and insurance design.Secondly,from the perspective of insurers’ game,this paper studies the non-zero-sum stochastic differential game problem of multiple mean-variance insurers in a market with mispricing and default risk.In this setting,insurers can not only buy proportional reinsurance,but also invest in risk-free assets,market indices,defaultable bonds,and multiple pairs of mispriced stocks.These mispriced stocks follow a "cointegrated system" and their expected returns are subject to a mean-reverting process,while bonds are subject to default risk.In particular,this paper assumes that only a few insurance companies can invest in mispriced stocks,which is more consistent with the reality and reflects the advantages brought by investment information in a competitive market.The objective of each insurer is to maximize its own relative performance wealth under the mean-variance criterion.Using stochastic control theory,the extended Hamilton-Jacobi-Bellman(HJB)equation is formulated and the analytic equilibrium strategy is successfully obtained.Further,it verifies the competitive advantage that insurers gain from investment opportunities in mispriced stocks.Different from the existing literature,this paper uses M-matrix to present the results,which is not only helpful to prove the existence and uniqueness of the solution,but also easy to carry out parameter sensitivity analysis.Thirdly,according to the realistic regulatory requirements for the insurance industry,the optimal capital allocation of insurance companies is considered,and a new generalized tail mean-variance(GTMV)model is proposed.This model uses Bregman divergence to construct the distance function between risk and capital,which can take into account the size and fluctuation of loss at the same time.This paper not only proves the existence and uniqueness of the optimal capital allocation,but also provides a system of general equations to which the optimal solutions obey.Furthermore,the Makovian tail mean-variance(MTMV)model is introduced,and the explicit optimal allocation formula independent of distribution is derived,which covers many existing capital allocation principles.In the specific application,the multivariate generalized hyperbolic distribution(MGH)is used to model the risk,and the analytical solution of the parameterization is derived.However,for the non-negative risk of the multivariate log-generalized hyperbolic distribution(log-MGH),explicit approximate solutions are obtained by using the convex bound approximation method.In addition,two numerical examples,namely the market risk analysis of the S&P 500 industry sector index and the evaluation of Australian insurance claims data,are used to demonstrate the effectiveness,robustness and accuracy of the capital allocation method in the paper.Finally,from the perspective of high-order risk management,we explore two new risk measures under the weighted risk aggregation model:tail moment(TM)and tail joint moment(TJM).These two measures contain many classical risk measures and can also quantify higher-order moment risks such as tail skewness and tail kurtosis.Considering that financial and insurance data are usually asymmetric and heavy-tailed,this paper adopts multivariate generalized hyperbolic distribution to model risk.In this framework,the analytical expressions of TM and TJM are derived,which greatly facilitates the assessment of portfolio tail risk and the analysis of tail correlation between risky assets.In addition,two empirical cases are used to demonstrate the advantages and robustness of TM and TJM in risk management and portfolio selection.In the first case,tail conditional skewness(TCS)and tail conditional kurtosis(TCK)are used to evaluate the tail distribution configuration and extreme loss risk.The second case focuses on the risk dependence in the downward market,and uses tail correlation(TCOR)and tail co-skewness(TCOS)to analyze the risk dependence between stocks and market indexes during the market decline,which provides an important reference for evaluating the tail risk of portfolio and hedging the downside market risk.更多还原