Insurance Mathematics & Economics最新文献

Experience rating in insurance uses a Bayesian credibility model to upgrade the current premiums of a contract by taking into account policyholders' attributes and their claim history. Most data-driven models used for this task are mathematically intractable, and premiums must be obtained through numerical methods such as simulation via MCMC. However, these methods can be computationally expensive and even prohibitive for large portfolios when applied at the policyholder level. Additionally, these computations become “black-box” procedures as there is no analytical expression showing how the claim history of policyholders is used to upgrade their premiums. To address these challenges, this paper proposes a surrogate modeling approach to inexpensively derive an analytical expression for computing the Bayesian premiums for any given model, approximately. As a part of the methodology, the paper introduces a likelihood-based summary statistic of the policyholder's claim history that serves as the main input of the surrogate model and that is sufficient for certain families of distribution, including the exponential dispersion family. As a result, the computational burden of experience rating for large portfolios is reduced through the direct evaluation of such analytical expression, which can provide a transparent and interpretable way of computing Bayesian premiums.

We propose the star-shaped acceptability indexes as generalizations of both the approaches of Cherny and Madan (2009) and Rosazza Gianin and Sgarra (2013) in the same vein as star-shaped risk measures generalize both the classes of coherent and convex risk measures in Castagnoli et al. (2022). We characterize acceptability indexes through star-shaped risk measures and star-shaped acceptance sets as the minimum of a family of quasi-concave acceptability indexes. Further, we introduce concrete examples under our approach linked to Value at Risk, risk-adjusted reward on capital, reward-based gain-loss ratio, and monotone reward-deviation ratio.

The Erlang mixture with a common scale parameter is one of many popular models for modeling insurance losses. However, the actuarial literature recognizes and discusses some limitations of aforementioned model in approximate heavy-tailed distributions. In this paper, a size-biased left-truncated Lognormal (SB-ltLN) mixture is proposed as a robust alternative to the Erlang mixture for modeling left-truncated insurance losses with a heavy tail. The weak denseness property of the weighted Lognormal mixture is studied along with the tail behavior. Explicit analytical solutions are derived for moments and Tail Value at Risk based on the proposed model. An extension of the regularized expectation–maximization (REM) algorithm with Shannon's entropy weights (ewREM) is introduced for parameter estimation and variability assessment. The Operational Riskdata eXchange's left-truncated internal fraud loss data set is used to illustrate applications of the proposed model. Finally, the results of a simulation study show promising performance of the proposed SB-ltLN mixture in different simulation settings.

This paper introduces a fair valuation framework for pricing variable annuity liabilities and their embedded guarantee riders within a dynamic multi-period context. We focus on variable annuities featuring the Guaranteed Lifetime Withdrawal Benefit (GLWB) rider, which exposes policyholders to both financial and longevity risks. We employ a fair dynamic valuation method that is market-consistent, actuarially-consistent, and time-consistent. Our findings demonstrate that this approach effectively establishes fair management fee rates, aligning with prior research and industry surveys. Furthermore, we highlight the potential for significant reductions in liability valuation, and consequently, GLWB rider pricing, through effective management of longevity risk within the insurer's net liability.

This paper presents novel characterization results for classes of law-invariant star-shaped functionals. We begin by establishing characterizations for positively homogeneous and star-shaped functionals that exhibit second- or convex-order stochastic dominance consistency. Building on these characterizations, we proceed to derive Kusuoka-type representations for these functionals, shedding light on their mathematical structure and intimate connections to Value-at-Risk and Expected Shortfall. Furthermore, we offer representations of general law-invariant star-shaped functionals as robustifications of Value-at-Risk. Notably, our results are versatile, accommodating settings that may, or may not, involve monotonicity and/or cash-additivity. All of these characterizations are developed within a general locally convex topological space of random variables, ensuring the broad applicability of our results in various financial, insurance and probabilistic contexts.

Dominance relations and diagnostic tools based on Lorenz and Concentration curves in order to compare competing estimators of the regression function have recently been proposed. This approach turns out to be equivalent to forecast dominance when the estimators under consideration are auto-calibrated. A new characterization of auto-calibration is established, based on the graphs of Lorenz and Concentration curves. This result is exploited to propose an effective testing procedure for auto-calibration. A simulation study is conducted to evaluate its performances and its relevance for practice is demonstrated on an insurance data set.

We study a non-concave optimization problem in which an insurance company maximizes the expected utility of the surplus under a risk-based regulatory constraint. The non-concavity does not stem from the utility function, but from non-linear functions related to the terminal wealth characterizing the surplus. For this problem, we consider four different prevalent risk constraints (Expected Shortfall, Expected Discounted Shortfall, Value-at-Risk, and Average Value-at-Risk), and investigate their effects on the optimal solution. Our main contributions are in obtaining an analytical solution under each of the four risk constraints in the form of the optimal terminal wealth. We show that the four risk constraints lead to the same optimal solution, which differs from previous conclusions obtained from the corresponding concave optimization problem under a risk constraint. Compared with the benchmark unconstrained utility maximization problem, all the four risk constraints effectively and equivalently reduce the set of zero terminal wealth, but do not fully eliminate this set, indicating the success and failure of the respective financial regulations.¹

We analyze how precautionary motives affect the decisions of a risk-averse agent on saving, labor supply and retirement. In a setting where there is a random shock which affects agent disutility from work, we show that uncertainty directly affects retirement age and saving, but leaves labor supply during working age unchanged. In particular, a precautionary motive for retirement always arises, which pushes the agent to bring forward retirement in the presence of a risk on the cost of work effort. Moreover, prudence and a sufficiently high level of absolute temperance are sufficient conditions for precautionary saving. In this setting, we also study the effects of two common reforms of the pension system: an increase in pension contributions and a cut in pension benefits. The conditions for the agent to postpone retirement and increase labor supply are studied. This makes it possible to characterize the circumstances when the financial soundness of the pension system improves after these reforms.

The four-parameter generalized beta distribution of the second kind (GBII) has been proposed for modeling insurance losses with heavy-tailed features. The aim of this paper is to present a parametric composite GBII regression modeling by splicing two GBII distributions using mode matching method. It is designed for simultaneous modeling of small and large claims and capturing the policyholder heterogeneity by introducing the covariates into the scale parameter. The threshold that splits two GBII distributions is allowed to vary across individuals policyholders based on their risk features. The proposed regression modeling also contains a wide range of insurance loss distributions as the head and the tail respectively and provides the close-formed expressions for parameter estimation and model prediction. A simulation study is conducted to show the accuracy of the proposed estimation method and the flexibility of the regressions. Some illustrations of the applicability of the new class of distributions and regressions are provided with a Danish fire losses data set and a Chinese medical insurance claims data set, comparing with the results of competing models from the literature.

This paper investigates a non-zero-sum stochastic differential game among n competitive CARA asset-liability managers, who are concerned about the potential model ambiguity and aim to seek the robust investment strategies. The ambiguity-averse managers are subject to uncontrollable and idiosyncratic random liabilities driven by generalized drifted Brownian motions and have access to an incomplete financial market consisting of a risk-free asset, a market index and a stock under a multivariate stochastic covariance model. The market dynamics permit not only stochastic correlation between the risky assets but also path-dependent and time-varying risk premium and volatility, depending on two affine-diffusion factor processes. The objective of each manager is to maximize the expected exponential utility of his terminal surplus relative to the average among his competitors under the worst-case scenario of the alternative measures. We manage to solve this robust non-Markovian stochastic differential game by using a backward stochastic differential equation approach. Explicit expressions for the robust Nash equilibrium investment policies, the density generator processes under the well-defined worst-case probability measures and the corresponding value functions are derived. Conditions for the admissibility of the robust equilibrium strategies are provided. Finally, we perform some numerical examples to illustrate the influence of model parameters on the equilibrium investment strategies and draw some economic interpretations from these results.