The paper develops a methodology to enable microscopic models of transportation systems to be accessible for a statistical study of traffic accidents. Our approach is intended to permit an understanding not only of historical losses but also of incidents that may occur in altered, potential future systems. Through such a counterfactual analysis, it is possible, from an insurance, but also from an engineering perspective, to assess the impact of changes in the design of vehicles and transport systems in terms of their impact on road safety and functionality.

Structurally, we characterize the total loss distribution approximatively as a mean-variance mixture. This also yields valuation procedures that can be used instead of Monte Carlo simulation. Specifically, we construct an implementation based on the open-source traffic simulator SUMO and illustrate the potential of the approach in counterfactual case studies.

The ratemaking process is a key issue in insurance pricing. It consists in pooling together policyholders with similar risk profiles into rating classes and assigning the same premium for policyholders in the same class. In actuarial practice, rating systems are typically not based on all risk factors but rather only some of factors are selected to construct the rating classes. The objective of this study is to investigate the selection of risk factors in order to construct rating classes that exhibit maximum internal homogeneity. For this selection, we adopt the Shapley effects from global sensitivity analysis. While these sensitivity indices are used for model interpretability, we apply them to construct rating classes. We provide a new strategy to estimate them, and we connect them to the intra-class variability and heterogeneity of the rating classes. To verify the appropriateness of our procedure, we introduce a measure of heterogeneity specifically designed to compare rating systems with a different number of classes. Using a well-known car insurance dataset, we show that the rating system constructed with the Shapley effects is the one minimizing this heterogeneity measure.

Modelling mortality co-movements for multiple populations has significant implications for mortality/longevity risk management. This paper assumes that multiple populations are heterogeneous sub-populations randomly drawn from a hypothetical super-population. Those heterogeneous sub-populations may exhibit various patterns of mortality dynamics across different age groups. We propose a hierarchical structure of these age patterns to ensure the model stability and use a Vector Error Correction Model (VECM) to fit the co-movements over time. Especially, a structural analysis based on the VECM is implemented to investigate potential interdependence among mortality dynamics of the examined populations. An efficient Bayesian Markov Chain Monte-Carlo method is also developed to estimate the unknown parameters to address the computational complexity. Our empirical application to the mortality data collected for the Group of Seven nations demonstrates the efficacy of our approach.

In this paper, we study the optimal VIX-linked target benefit (TB) pension design. By applying the dynamic programming approach, we show the optimal risk-sharing structure for the benefit payment exhibits a linear form that consists of three components: (1) a model-robust performance adjustment, (2) a counter-cyclical volatility adjustment that depends on the VIX index, and (3) a TB level that is partially indexed to the cost-of-living adjustment. Differences between our results and the previous literature are highlighted via both theoretical derivations and numerical illustrations.

We consider the holder of an individual tontine retirement account, with maximum and minimum withdrawal amounts (per year) specified. The tontine account holder initiates the account at age 65 and earns mortality credits while alive, but forfeits all wealth in the account upon death. The holder wants to maximize total withdrawals and minimize expected shortfall at the end of the retirement horizon of 30 years (i.e., it is assumed that the holder survives to age 95). The holder controls the amount withdrawn each year and the fraction of the retirement portfolio invested in stocks and bonds. The optimal controls are determined based on a parametric model fitted to almost a century of market data. The optimal control algorithm is based on dynamic programming and the solution of a partial integro differential equation (PIDE) using Fourier methods. The optimal strategy (based on the parametric model) is tested out of sample using stationary block bootstrap resampling of the historical data. In terms of an expected total withdrawal, expected shortfall (EW-ES) efficient frontier, the tontine overlay dramatically outperforms an optimal strategy (without the tontine overlay), which in turn outperforms a constant weight strategy with withdrawals based on the ubiquitous four per cent rule.

We study the optimal investment-reinsurance problem in the context of equity-linked insurance products. Such products often have a capital guarantee, which can motivate insurers to purchase reinsurance. Since a reinsurance contract implies an interaction between the insurer and the reinsurer, we model the optimization problem as a Stackelberg game. The reinsurer is the leader in the game and maximizes its expected utility by selecting its optimal investment strategy and a safety loading in the reinsurance contract it offers to the insurer. The reinsurer can assess how the insurer will rationally react on each action of the reinsurer. The insurance company is the follower and maximizes its expected utility by choosing its investment strategy and the amount of reinsurance the company purchases at the price offered by the reinsurer. In this game, we derive the Stackelberg equilibrium for general utility functions. For power utility functions, we calculate the equilibrium explicitly and find that the reinsurer selects the largest reinsurance premium such that the insurer may still buy the maximal amount of reinsurance. Since in the equilibrium the insurer is indifferent in the amount of reinsurance, in practice, the reinsurer should consider charging a smaller reinsurance premium than the equilibrium one. Therefore, we propose several criteria for choosing such a discount rate and investigate its wealth-equivalent impact on the expected utility of each party.

Pension funds and insurers face difficulties in hedging their longevity risk, which is the uncertainty of how long their clients will live. A possible solution could be using longevity-linked securities to transfer some of this risk to other parties. However, these securities may not match the actual mortality rates of the insurer’s clients, resulting in a potential loss due to basis risk. In this paper, we measure this basis risk through the pricing of a longevity derivative under Solvency II. We also compare this method with other common pricing methods in finance. We explore and evaluate different hedging strategies for insurers, using a multi-population model derived from a two-dimensional Hull and White model that captures the dynamics of mortality over time.

This paper considers variable annuity (VA) contracts embedded with guaranteed minimum accumulation benefit (GMAB) riders when policyholder’s proceeds are taxed upon early surrender or maturity. These contracts promise the return of the premium paid by the policyholder, or a higher rolled-up value, at the end of the investment period. A partial differential equation valuation framework which exploits the numerical method of lines is used to determine fair fees that render the policyholder and insurer breakeven. Two taxation regimes are considered: one where capital gains are allowed to offset losses and a second where gains do not offset losses. Most insurance providers highlight the tax-deferred features of VA contracts. We show that the regime under which the insured is taxed significantly impacts prices. If losses are allowed to offset gains then this enhances the market, increasing the policyholder’s willingness to participate in the market compared to the case when losses are not allowed to offset gains. With fair fees from the policyholder’s perspective, we show that the net profit is generally positive for insurance companies offering the contract as a naked option without any hedge. We also show how investment policy, as reflected in the Sharpe ratio, impacts and interacts with policyholder persistency.