Insurance & Actuarial Risk

This article explores the potential of generative AI (GenAI) to support actuarial practice through four implemented case studies. It situates these case studies within the broader evolution of artificial intelligence in actuarial science, from early neural networks and machine learning to modern tra

This paper investigates the dynamic reinsurance design problem under the mean-variance criterion, incorporating heterogeneous beliefs between the insurer and the reinsurer, and introducing an incentive compatibility constraint to address moral hazard. The insurer’s surplus process is modeled using t

This paper studies the robust reinsurance and investment games for competitive insurers. Model uncertainty is characterized by a class of equivalent probability measures. Each insurer is concerned with relative performance under the worst-case scenario. Insurers’ surplus processes are approximated b

This paper explores optimal insurance solutions based on the Lambda-Value-at-Risk ($Λ\VaR$). If the expected value premium principle is used, our findings confirm that, similar to the VaR model, a truncated stop-loss indemnity is optimal in the $Λ\VaR$ model. We further provide a closed-form express

We find the optimal indemnity to maximize the expected utility of terminal wealth of a buyer of insurance whose preferences are modeled by an exponential utility. The insurance premium is computed by a convex functional. We obtain a necessary condition for the optimal indemnity; then, because the ca

The collective risk model differentiates usually between claims frequencies (and their distribution) and claim sizes (and their distribution). For the claims frequencies typically classical discrete distributions are considered, such as Binomial-, Negative binomial- or Poisson distributions. Since t

We study multidimensional Cramér-Lundberg risk processes where agents, located on a large sparse network, receive losses form their neighbors. To reduce the dimensionality of the problem, we introduce classification of agents according to an arbitrary countable set of types. The ruin of any agent tr

We address the problem of sharing risk among agents with preferences modelled by a general class of comonotonic additive and law-based functionals that need not be either monotone or convex. Such functionals are called distortion riskmetrics, which include many statistical measures of risk and varia

In this paper, we study a dual risk model with delays in the spirit of Dassios-Zhao. When a new innovation occurs, there is a delay before the innovation turns into a profit. We obtain large initial surplus asymptotics for the ruin probability and ruin time distributions. For some special cases, we

In most cases, insurance contracts are linked to the financial markets, such as through interest rates or equity-linked insurance products. To motivate an evaluation rule in these hybrid markets, Artzner et al. (2022) introduced the notion of insurance-finance arbitrage. In this paper we extend thei

This manuscript formalizes the most popular model validation tools used in general insurance actuarial modeling. These include graphical tools like calibration plots, actual-vs-expected plots, lift charts, Murphy diagrams, as well as classical statistical tools such as Bregman losses, deviance losse

We propose a peer-to-peer (P2P) insurance scheme comprising a risk-sharing pool and a reinsurer. A plan manager determines how risks are allocated among members and ceded to the reinsurer, while the reinsurer sets the reinsurance loading. Our work focuses on the strategic interaction between the pla

This paper investigates optimal withdrawal strategies and behavior of policyholders in a variable annuity (VA) contract with a guaranteed minimum withdrawal benefit (GMWB) rider incorporating taxation and a ratchet mechanism for enhancing the benefit base during the life of the contract. Mathematica

We mathematically demonstrate how and what it means for two collective pension funds to mutually insure one another against systematic longevity risk. The key equation that facilitates the exchange of insurance is a market clearing condition. This enables an insurance market to be established even i

The frequent occurrence of cyber risks and their serious economic consequences have created a growth market for cyber insurance. The calculation of aggregate losses, an essential step in insurance pricing, has attracted considerable attention in recent years. This research develops a path-based k-ge

This paper examines the retirement decision, optimal investment, and consumption strategies under an age-dependent force of mortality. We formulate the optimization problem as a combined stochastic control and optimal stopping problem with a random time horizon, featuring three state variables: weal

In order to deal with the aging problem, pension system is actively transformed into the funded scheme. However, the funded scheme does not completely replace PAYGO (Pay as You Go) scheme and there exist heterogeneous mixes among PAYGO, EET (Exempt, Exempt, Taxed) and individual savings in different

If individuals at the highest mortality risk are also least likely to lapse a life insurance policy, then lapse-supported premiums magnify adverse selection costs. As an example, we model ‘Term to 100’ contracts, and risk as revealed by genetic test results. We identify three methods of managing lap

This study examines how market risks impact the sustainability and performance of the New Pension System (NPS). NPS relies on defined contributions from both employees and employers to build a corpus during the employee’s service period. Upon retirement, employees use the corpus fund to sustain thei

In this paper, we study an optimal mean-variance investment-reinsurance problem for an insurer (she) under a Cramér-Lundberg model with random coefficients. At any time, the insurer can purchase reinsurance or acquire new business and invest her surplus in a security market consisting of a risk-free