Hansjörg Albrecher

We examine the key challenges associated with insuring climate-related risks in the context of a changing climate. Adopting a balance-sheet perspective on insurance company management, we analyze the concept of insurability and how it may be reshaped by climate change. Focussing on non-life perils, we further explore the roles of regulation, risk prevention and mitigation in addressing these issues, and discuss a range of potential solutions – and limitations – that emerge. These challenges also open up interesting opportunities for both academic research and practical innovation within the insurance industry.

Achieving net-zero carbon emissions requires a transformation of energy systems, industrial processes, and consumption patterns. In particular, a transition towards that goal involves a gradual reduction of excess carbon emissions that are not essential for the well-functioning of society. In this paper we study this problem from a stochastic control perspective to identify the optimal gradual reduction of the emission rate, when an allocated excess carbon budget is used up over time. Assuming that updates of the available carbon budget follow a diffusion process, we identify the emission strategy that maximizes the expected discounted future profit from these excess emissions under the constraint of a non-increasing emission rate, with an additional term rewarding the amount of time for which the excess carbon budget is not yet depleted. We establish a link of this topic to optimal dividend problems in insurance risk theory under ratcheting constraints and show that the value function is the unique viscosity solution of the associated Hamilton-Jacobi-Bellman equation. We provide numerical illustrations of the resulting optimal abatement schedule of emissions and a quantitative evaluation of the effect of the non-increasing rate constraint on the value function.

In this paper, we study a queueing process for which the dynamics are changed once the workload in the queue exceeds a predefined threshold, and these new dynamics stay in force until the queue is emptied, at which point the previous dynamics are again reinstalled. For general spectrally positive Lévy processes in each case, we derive expressions for the workload at an independent exponentially distributed random time horizon and study in detail properties of the workload in stationarity. We work out explicit formulas as well as expressions for the optimal changing threshold for special cases of the underlying process dynamics and a chosen set of involved switching, holding, and service cost functions. Funding: The research of O. Boxma and M. Mandjes has been partly funded by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek Gravitation [Project Networks, Grant 024.002.003]. The research of O. Kella is partially funded by Israel Science Foundation [Grant 3336/24] and the Vigevani Chair in Statistics.

In this paper, we investigate how policyholder information and broader economic conditions jointly influence the duration of credit life insurance contracts in the French market. Employing a proportional-intensities regression framework built on inhomogeneous phase-type distributions, we capture the way covariates shape the distribution of policy lifetime until a lapse occurs. The model is estimated via a specialized expectation-maximization algorithm, adapted to handle censored data, covariates, and feature selection through shrinkage. Our analysis of real-world data shows that different policyholder attributes and economic factors can significantly alter lapse behavior, with effects varying across insurance products, individuals, and economic cycles. These findings highlight the importance of integrating both individual-level and macroeconomic indicators in lapse risk assessment, ultimately informing more accurate pricing and allowing for improved risk management strategies.

Cost-of-capital valuation is a well-established approach to the valuation of liabilities and is one of the cornerstones of current regulatory frameworks for the insurance industry. Standard cost-of-capital considerations typically rely on the assumption that the required buffer capital is held in risk-less one-year bonds. The aim of this work is to analyze the effects of allowing investments of the buffer capital in risky assets, for example, in a combination of stocks and bonds. In particular, we make precise how the decomposition of the buffer capital into contributions from policyholders and investors varies as the degree of riskiness of the investment increases and highlight the role of limited liability in the case of heavy-tailed insurance risks. With a focus on nonlife insurance, we present a combination of general theoretical results, explicit results for certain stochastic models, and numerical results that emphasize the key findings.

Achieving net-zero carbon emissions requires a transformation of energy systems, industrial processes, and consumption patterns. In particular, a transition towards that goal involves a gradual reduction of excess carbon emissions that are not essential for the well-functioning of society. In this paper we study this problem from a stochastic control perspective to identify the optimal gradual reduction of the emission rate, when an allocated excess carbon budget is used up over time. Assuming that updates of the available carbon budget follow a diffusion process, we identify the emission strategy that maximizes expected discounted emissions under the constraint of a non-increasing emission rate, with an additional term rewarding the amount of time for which the budget is not yet depleted. We establish a link of this topic to optimal dividend problems in insurance risk theory under ratcheting constraints and show that the value function is the unique viscosity solution of the associated Hamilton-Jacobi-Bellman equation. We provide numerical illustrations of the resulting optimal abatement schedule of emissions and a quantitative evaluation of the effect of the non-increasing rate constraint on the value function.

Hybrid stochastic differential equations (SDEs) are a useful tool for modeling continuously varying stochastic systems modulated by a random environment, which may depend on the system state itself. In this paper we establish the pathwise convergence of solutions to hybrid SDEs using space-grid discretizations. Though time-grid discretizations are a classical approach for simulation purposes, our space-grid discretization provides a link with multi-regime Markov-modulated Brownian motions. This connection allows us to explore aspects that have been largely unexplored in the hybrid SDE literature. Specifically, we exploit our convergence result to obtain efficient and computationally tractable approximations for first-passage probabilities and expected occupation times of the solutions to hybrid SDEs. Lastly, we illustrate the effectiveness of the resulting approximations through numerical examples.

We provide a survey of how techniques developed for the modelling of extremes naturally matter in insurance, and how they need to and can be adapted for the insurance applications. Topics covered include truncation, tempering, censoring and regression techniques. The discussed techniques are illustrated on concrete data sets.

We study optimal dividend strategies for an insurance company facing natural catastrophe claims, anticipating the arrival of a climate tipping point after which the claim intensity and/or the claim size distribution of the underlying risks deteriorates irreversibly. For shot‐noise Cox claim arrivals, we show that the nonstationary feature of such a tipping point can be an advantage for shareholders. Assuming the tipping point arrives according to an Erlang distribution, we demonstrate that the corresponding system of two‐dimensional stochastic control problems admits a viscosity solution, which can be numerically approximated in an efficient way. The results are illustrated through several numerical examples. Also, the sensitivity of the optimal dividend strategies to the presence of a climate tipping point is analyzed.