Extreme cold temperature events have long been associated with excess mortality via many different causes of death. Climate change is expected to intensify the frequency and severity of these extreme temperature events. To quantify and model cold-related excess deaths and, in turn, to better understand the potential impact of climate change on future mortality levels, we propose a new approach based on the state-of-the-art stationary vine copulas. We adopt the S-vine model for the first time in the context of climate-driven mortality risk, and introduce a special case of the model to aid model comparison and enhance interpretability of the results. This model is referred to as a (stationary) centrally connected C-vine (CCC-vine). Three types of dependence are captured by the proposed models, which are temporal dependence, contemporaneous cross-sectional dependence, and non-contemporaneous cross-sectional dependence. We fit the CCC-vine model to the US regional cause-specific death data over the period 1999–2018 and conclude that the model outperforms various benchmark models including the Gaussian copula model and the VAR model. Based on the fitted models, we generate several temperature scenarios and assess cause-specific excess deaths and overall excess deaths due to extreme cold temperatures. We also analyze and compare the geographical differences in cold-related excess deaths across six continental US regions. The results from our study can help public health interventions during extreme cold events to reduce temperature-driven excess deaths.

Actuarial literature contains countless formulations and analytical results of optimal reinsurance for a single risk, but there is limited research on optimal solutions when the cedent runs many lines of business and is asked to manage the total risk in a certain integrated sense. In this paper, we extend the problem of optimal reinsurance to a multivariate framework where the cedent has multiple risks that cannot be bundled together into one. More specifically, we optimize layer contracts using a more industrially based criterion, where risk and profit are balanced through a ratio between the value-at-risk and the expected surplus. The effects of the marginal risk distributions and the dependence structure, as well as of the premium principle, are investigated. Using convexity theory, we show that the optimal solution is strongly related to the monotonicity property of the hazard rate functions of the risks. For decreasing hazard rates the solution can typically be found by Lagrangian optimization, while for increasing hazard rates, one often ends up with an extreme point solution, where at least one of the contracts is a stop-loss one. Further, the joint optimization of the contracts results in a better balance between risk and expected gain than when the contracts are optimized separately, even when the risks are independent. This advantage increases with the dependence between the risks, as well as when the marginal risk distributions become more heavy-tailed.

In this paper, we provide generalizations of the functional equations that characterize the lack-of-memory properties: more specifically, we extend the univariate functional equation introduced by Kaminsky (1983, An aging property of the Gompertz survival function and a discrete analog (Tech. Rep.). Department of Mathematical Statistics, University of Umeå, Sweden) and the corresponding bivariate strong and weak versions studied in Marshall and Olkin (2015, A bivariate Gompertz–Makeham life distribution. Journal of Multivariate Analysis, 139, 219–226. https://doi.org/10.1016/j.jmva.2015.02.011) by allowing the conditional survival distribution to be a fully general time dependent distortion of the unconditional one. Since the univariate functional equation leads only to a trivial case and the solutions of the strong bivariate functional equation have been already studied in the literature, the analysis focuses on the weak bivariate case, where joint residual lifetimes are conditioned on survival beyond a common threshold t. In view of potential applications to insurance risk analysis, we study the impact of the time dependent distortion on the aging properties and on the dependence structure of the residual lifetimes via time-varying Kendall's function and tail dependence coefficients: moreover, we provide some illustrative examples showing that these distributions can model both broken hearth effect as well as its reverse version.

Laplace approximation provides a Gaussian approximation of a posterior distribution via a second-order Taylor expansion. Although the Bernstein–von Mises theorem guarantees asymptotic normality as the sample size approaches infinity, the Gaussian approximation may be unreliable when the sample size is finite. This is particularly true when the posterior distribution is skewed, which is a common occurrence in the insurance ratemaking process, where the use of a Gaussian distribution may not yield an accurate approximation. In this study, by utilizing the generalized version of Taylor expansion [Widder (1928). A generalization of Taylor's series. Transactions of the American Mathematical Society, 30(1), 126–154], we introduce a generalized version of Laplace approximation where the posterior distribution is approximated by various parametric distributions in the exponential family. We apply this method to random effects models, connecting it to credibility premium, in the insurance context. While credibility premium provides an affine posterior mean approximation, it lacks further distributional information. Our method introduces the ability to approximate the posterior distribution, while still providing the same point approximation as credibility premium. Numerical analysis confirms the effectiveness of the proposed approach.

In this paper, we address an optimal stochastic asset allocation and reinsurance problem in continuous-time contagious financial and insurance markets. The insurer is subject to contagious claims, which are modeled using an enhanced dynamic contagion process. This process generalizes the externally-exciting Cox process with shot noise and the self-exciting Hawkes process while also capturing the dependence structure between the financial and insurance markets. Furthermore, the insurer is assumed to be ambiguity-averse, with distinct modeling risk aversion preferences for the risky asset, extreme external events, and contagious insurance claims. The insurer aims to maximize the expected utility of the terminal surplus and a specified penalty function at a fixed terminal date under the worst-case scenario. Using the dynamic programing principle, we derive the extended Hamilton-Jacobi-Bellman (HJB) equation and develop an iterative numerical scheme to compute the value function and optimal controls. The convergence of the numerical method is rigorously proven. To support our quantitative analysis, we provide several numerical examples illustrating the impact of the dependence structure and ambiguity aversion on optimal controls.

This paper examines portfolio insurance (PI) problems for investors who require a minimum level of consumption. Its key contribution is introducing the Option-Based Portfolio and Consumption Insurance (OBPCI) strategy, which extends the popular OBPI framework. As the optimal solution to a constrained utility maximization problem under a general local covariance model, OBPCI is derived using the martingale approach and can be interpreted as a portfolio of options. Given the lack of valid benchmarks involving consumption in the literature, we also introduce and formalize two competitive strategies, optimal on their own, albeit suboptimal to our main problem: the Synthetic Constant Proportion Portfolio and Consumption Insurance (SCPPCI) and the Synthetic Option-Based Portfolio and Consumption Insurance (SOBPCI). Our numerical analysis shows that, under realistic parameters, SCPPCI and SOBPCI can lead to equivalent welfare losses of up to 9 % for a short investment horizon and 5 % for low risk aversion, respectively, relative to OBPCI.

This paper investigates the optimal control problem of ratcheting dividend with capital injection under a Brownian risk model. We show that the value function is the unique viscosity solution to the associated Hamilton–Jacobi–Bellman equation. Explicit analytical expressions of the value function and the optimal strategy are obtained when the general ratcheting dividend strategies are restricted as finite ratcheting dividend strategies (i.e. the dividend rate takes only a finite number of values), where the optimal dividend strategy is the threshold-type finite ratcheting dividend strategy, and the optimal capital injection strategy is the bailout strategy. Some numerical illustrations are provided at the end.

This article studies a mean-variance Stackelberg game between an insured and an insurer under a self-protection model, where the insured's effort is observable by the insurer and reflected in the insurance premium. We adopt a proportional insurance model under a quadratic premium principle and incorporate a cost-sharing mechanism for self-protection. The existence of equilibrium solutions for insurance demand, self-protection effort, and cost-sharing proportions is established, and their interactions are analyzed theoretically. Numerical analysis reveals conditions under which self-protection and market insurance act as complementary or substitutable risk management tools.

This paper develops a novel and flexible life-cycle framework, where borrowing human capital plays an explicit role in modeling and decision-making, explicitly impacting risk-aversion levels, borrowing rates, and inter-temporal discount rates. We find the pre-commitment solution to this new ‘double’ optimization problem in semi-closed form in a region of the control/policy space while developing a numerical procedure to approximate the remaining region using the solvable cases. We carry out numerical case studies revealing two unprecedented conclusions. First, the optimal level of human capital borrowings depends non-trivially on many characteristics of the investor and the market, e.g. range of borrowing cost and risk aversion, subjective discount rate, future income level, and size of their initial endowment. Second, we observe a high level of welfare losses when investors fail to take advantage of their human capital; for instance, investors with high endowment could experience a welfare loss exceeding 70%, while investors with high income could see a 20% welfare loss.

Population forecasting is critical for actuarial practice, particularly in assessing longevity risk, pricing life annuities, and evaluating pension fund sustainability. Traditional cohort component methods face dimensionality challenges when projecting age- and gender-specific populations for large countries with limited data. In this work, we propose a Factor-augmented Cohort Component Method (FaCCM) that integrates time-varying Leslie matrices with factor modeling to generate mid-to-long-term probabilistic forecasts. Unlike existing approaches, our method requires only census data, avoids restrictive parametric assumptions, and quantifies uncertainties via bootstrapped prediction intervals, which is crucial for actuarial applications such as measuring pension deficits and designing cohort-specific annuities. We validate the FaCCM's performance using simulations and real data, and demonstrate its ability to interpret latent factors driving changes in fertility (e.g. delayed childbearing), improvements in mortality, and shifts in migration patterns. Finally, we apply the FaCCM to China's aging population, projecting demographic shifts through 2060 and quantifying the financial impact of the 2025 retirement delay policy. Our analysis reveals that raising the retirement age to 63 for men and 58 for women reduces the old-age dependency ratio by 15% by 2040, yet is insufficient to stabilize the pay-as-you-go pension expenditures.