This article examines a stochastic differential proportional reinsurance game under model uncertainty, framed within a Stackelberg game where one reinsurer and n insurers, all assumed to be ambiguity-averse, interact. The reinsurer, acting as the leader, seeks to maximize the expected utility of the combined terminal wealth of all players, rather than its own utility. The reinsurer controls risk pooling and determines insurers' risk quotas through risk adjustment coefficients. The insurers, in turn, manage their risks and expand their underwriting capacity by purchasing reinsurance and adopting strategies based on relative performance in a non-zero-sum stochastic differential game. Using dynamic programming and backward induction, we derive explicit expressions for the robust equilibrium strategies. Through numerical simulations, the article presents a comparative static analysis of the equilibrium strategies. The results show that the risk adjustment coefficient is positively correlated with the reinsurance premium and negatively correlated with the reinsurance ratio. As business correlation increases, the reinsurer reallocates a more significant portion of the risk quota to the lower risk insurer, optimizing risk distribution and improving overall portfolio management. Additionally, we observe that higher ambiguity aversion leads to more conservative reinsurance strategies, which in turn affect the reinsurer's premium-setting behavior.

We develop a verification theorem for infinite-horizon optimal stopping under G-Brownian motion and apply it to several stopping problems of economic interest. The theorem gives sufficient conditions under which a candidate solution to a system of variational inequalities is the value function under volatility, covariance, or joint drift–volatility ambiguity. In the canonical irreversible investment problem, volatility ambiguity advances investment because the worst-case scenario selects the lowest feasible volatility for a convex continuation value. Ambiguity about volatility therefore acts in the opposite direction from volatility itself, which postpones investment. In other environments, worst-case volatility can vary with the state, alter project relevance, create bilateral valuation wedges, shorten search, and change two-dimensional investment payoffs through covariance and correlation ambiguity. A common convexity-based mechanism drives these results: volatility ambiguity changes the perceived dispersion of future outcomes, whereas drift ambiguity acts through monotonicity.

This article investigates a trilateral stochastic differential reinsurance and investment game with heterogeneous reinsurance premiums. As the leader in the Stackelberg game, the reinsurer maximizes the expected utility of the combination of the three players' terminal wealth other than its own utility. The degree to which a reinsurer pays attention to an insurer depends on the coefficient alpha i(i=1,2). The insurers spread their risks and expand their underwriting capacity by purchasing reinsurance with strategies involving relative performance in a non-zero-sum stochastic differential game. We derive explicit expressions of the Nash equilibrium strategy and prove the verification theorem using dynamic programming and backward induction methods. We discuss the parameters comparative static analysis of the equilibrium strategies through numerical examples. The numerical results show that the coefficient alpha i(i=1,2) is proportional to the reinsurance premium price and is inversely proportional to the reinsurance ratio.

This paper explores the implications of using machine learning models in the pricing of catastrophe (CAT) bonds. By integrating advanced machine learning techniques, our approach uncovers nonlinear relationships and complex interactions between key risk factors and CAT bond spreads – dynamics that are often overlooked by traditional linear regression models. Using primary market CAT bond transaction records between January 1999 and March 2021, our findings demonstrate that machine learning models not only enhance the accuracy of CAT bond pricing but also provide a deeper understanding of how various risk factors interact and influence bond prices in a nonlinear way. These findings suggest that investors and issuers can benefit from incorporating machine learning to better capture the intricate interplay between risk factors when pricing CAT bonds. The results also highlight the potential for machine learning models to refine our understanding of asset pricing in markets characterized by complex risk structures.

. In order to more comprehensively describe the uncertain factors that affect interest rate changes in the financial market, this paper proposes an uncertain generalized mean reversion interest rate risk model based on uncertainty theory and studies the solution via its inverse uncertainty distribution of the model. On this basis, this paper also studies the applications of this model in zero-coupon bonds, interest rate ceilings, and interest rate floors. Besides, we design corresponding numerical algorithms to calculate the prices of the corresponding contracts. Finally, this paper conducts an empirical study based on China's two-year treasury bond interest rate data to verify the model's effectiveness. The numerical results show the proposed uncertain interest rate risk model fits the data well.

Aligning Large Language Models (LLMs) with human feedback is crucial for their development. Existing preference optimization methods such as DPO and KTO, while improved based on Reinforcement Learning from Human Feedback (RLHF), are inherently derived from PPO, requiring a reference model that adds GPU memory resources and relies heavily on abundant preference data. Meanwhile, current preference optimization research mainly targets single-question scenarios with two replies, neglecting optimization with multiple replies, which leads to a waste of data in the application. This study introduces the MPPO algorithm, which leverages the average likelihood of model responses to fit the reward function and maximizes the utilization of preference data. Through a comparison of Point-wise, Pair-wise, and List-wise implementations, we found that the Pair-wise approach achieves the best performance, significantly enhancing the quality of model responses. Experimental results demonstrate MPPO's outstanding performance across various benchmarks. On MT-Bench, MPPO outperforms DPO, ORPO, and SimPO. Notably, on Arena-Hard, MPPO surpasses DPO and ORPO by substantial margins. These achievements underscore the remarkable advantages of MPPO in preference optimization tasks.

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This paper investigates continuous-time intertemporal liabilitydriven investment strategies in the presence of liability constraints in a regimeswitching market. We employ the value of the liability portfolio as a natural numeraire rather than a traditional surplus to study the liability-driven optimal investment using the mean-variance criterion. Using the stochastic linear-quadratic control method, we obtain the closed-form optimal investment strategy and efficient frontiers to this problem. The solution involves a three-fund separation theorem based on investment in two underlying building blocks, the performance seeking portfolio and a liability hedging portfolio, in addition to the risk-free asset. That provides formal justification for liabilitydriven investment solutions offered by investment banks, insurance companies, and asset management firms under regime-switching environment. The optimal allocation strategy has a distinct cross-regime effect, both in terms of the components of the optimal allocation and their weights. Finally, the numerical analysis shows that the larger the initial asset-liability ratio and maturity are, the greater the terminal asset-liability ratio under the same risk level. The effects of parameters on liability-driven investment strategies vary according to different market states. Expected asset-liability structure, self-owned assetliability structure, time horizon, and the transition rate from a bearish to a bullish regime have a more significant impact on optimal portfolio allocation in a bearish regime than in a bullish regime. The asset-liability structure is more vulnerable to fluctuations in a bearish market than in a bullish market.

Using China's 2008 corporate tax reform as a quasi-natural experiment, we construct a difference-in-differences setting to study firms' asymmetric tax compliance. Compared to firms whose taxes were unaffected by the reform, firms whose tax rate increased reported significantly lower profit margins to avoid paying more taxes. However, firms facing a tax cut did not behave differently from the unaffected firms. The asymmetric behavior is valid for private firms, but not for state-owned firms that have softer budget constraints. Such tax avoidance is done through the manipulation of the costs of goods sold and other expenses, rather than managing net receivables.

Different from traditional asset-liability management where only investment allocation is considered, this paper introduces policy product allocation into asset-liability management of insurance companies. In order to balance product allocation and investment allocation, a bi-level optimization model is employed. Since the decision-making environment of the two allocation processes is full of indeterminacy, the imprecise information of the model is measured by uncertain variables in order to deal with the lack of enough historical data. To solve this bi-level Optimization problem containing uncertain variables, an uncertain bilevel programming model is used. Furthermore, we simulate a scenario to compare the bi-level optimization approach with other approaches by virtue of hybrid intelligent algorithms.

This paper considers a state-dependent optimal asset-liability management problem in continuous-time settings. The investor maximizes the expected state-dependent utility of the terminal asset-liability ratio in a regime-switching market to better describe insurance companies' needs for asset-liability matching and regulation with background risk. We apply the stochastic dynamic programming method to get closed-form results. We find that the optimal strategy in the state-dependent utility case is the same, and the optimal value function differs from the state-independent utility case. Finally, we study how the parameters impact the optimal investment strategy and corresponding value functions through numerical examples.

本文建立了人口结构变化、税费改革过程中开征遗产税的一般均衡世代交叠模型,以分析人口老龄化、生育率变化以及所得税、养老保险缴费率等税费制度改革对遗产倾向的影响,进而根据遗产倾向分析了遗产税对政府税收收入、未来劳均产出和个人终身效用的影响.分析表明:①代表性消费者年轻时期可支配收入的税费减少会弱化其遗产倾向,而养老保险个人账户缴费率降低则会强化其遗产倾向,老龄化程度加深、生育率降低也会强化其遗产倾向.②在配合调整个人所得税税率的情况下,开征遗产税的确有利于社会公平,它使得代表性消费者的终身效用取决于个人缴纳完社会基本养老保险后的工资与获得遗产的相对状况.③总体而言,税费率的影响要大于老龄化的影响,但小于生育率的影响.在一定的人口结构下,适时征收遗产税有益于政府税收、未来劳均产出和社会公平.

This article describes a robust continuous-time asset-liability management problem under Markov regime-switching. First, we employ the "homothetic robustness" to preserve the performance of robustness for the ALM model, which runs well in precisely modified state variables and performs reasonably if some forms of model misspecification exist. Second, we consider the asset-to-liability ratio instead of the surplus, which ensures that we use relative values instead of absolute values to modify the wealth process. Besides, we use the stochastic dynamic programming method to get some closed-form results and analyze the impacts of parameters on the investment strategy and value function, respectively, by numerical examples.

随着养老保障制度的完善和生育观念的转变,我国家庭的储蓄-教育权衡模式正逐渐发生变化,本文通过理论模型、实证检验和数值模拟对此进行了研究.理论研究表明:对于具有子代质量偏好的代表性消费者,统筹账户缴费率上升对其储蓄和子女教育投入均存在挤出效应;个人账户缴费率上升对子女教育投入没有影响,对储蓄存在挤出效应;子代质量偏好程度上升对储蓄存在挤出效应.实证检验表明:子代质量偏好和养老保险对流动人口家庭的储蓄行为影响不足.为解决养老保险基金的支付危机,政府政策选择的优先级依次是:出台措施缓解少子化危机、以财政补充养老保险基金、提高个人账户缴费率、提高统筹账户缴费率.本文为分析当前我国家庭的经济决策模式、缓解养老保险基金支付危机的政策选择提供了理论支撑.

本文使用两步共同随机前沿法对我国寿险公司创新能力进行测度,在此基础上,利用2010年～2019年我国寿险公司非平衡面板数据,使用两步差分广义矩估计方法对市场竞争与寿险公司创新能力之间的关系进行探讨.结果 显示,在我国寿险市场,竞争程度与公司创新能力具有显著的倒U型关系,在市场竞争强度由不足向过度竞争变化时,寿险公司创新能力先上升后下降,且这种关系在时间上是稳健的.另外,我国寿险市场竞争程度处于倒U型曲线左半部分,竞争程度尚有不足,因此本文建议监管部门应保持市场的适度竞争,实施多样化的创新激励政策,并加强知识产权保护力度.

Repeated history of pandemics, such as SARS, H1N1, Ebola, Zika, and COVID-19, has shown that pandemic risk is inevitable. Extraordinary shortages of medical resources have been observed in many parts of the world. Some attributing factors include the lack of sufficient stockpiles and the lack of coordinated efforts to deploy existing resources to the location of greatest needs. The paper investigates contingency planning and resources allocation from a risk management perspective, as opposed to the prevailing supply chain perspective. The key idea is that the competition of limited critical resources is not only present in different geographical locations but also at different stages of a pandemic. This paper draws on an analogy between risk aggregation and capital allocation in finance and pandemic resources planning and allocation for healthcare systems. The main contribution is to introduce new strategies for optimal stockpiling and allocation balancing spatio-temporal competitions of medical supply and demand.

This paper is devoted to evaluating the convertible bonds within the framework of uncertainty theory. Under the assumption that the underlying stock price follows an uncertain differential equation driven by Liu process, the price formulas of convertible bonds and the callable convertible bonds are derived by using the method of uncertain calculus. Finally, two numerical examples are discussed.

In this paper, we build an optimal control model with the objective to maximize the expected value of the time discount utility by selecting optimal investment, liability and dividend strategies for insurance companies. We then use the techniques from Merton (J Econ Theory 3(4):373–413, 1971) to solve our optimal control problem and deduce the optimal control solutions. Finally, we analyze the economic impacts on the optimal controls of the parameters in insurance market.

Uncertain differential equations are a type of differential equations driven by Liu processes. How to estimate the parameters in an uncertain differential equation based on the observed data is a crucial problem in the real applications of these equations. By means of the least squares estimation, this article proposes a principle of minimum noise as an approach to the problem. Following this principle, the estimates of the parameters in some special types of uncertain differential equations are derived, which are represented as functions of the observed data. In addition, some numerical experiments are performed to illustrate the principle.