Insurance Mathematics & Economics最新文献

This paper considers a risk-neutral insurer and a risk-averse individual who bargain over the terms of an insurance contract. Under asymmetric Nash bargaining, we show that the Pareto-optimal insurance contract always contains a straight deductible under linear transaction costs and that the deductible disappears if and only if the deadweight cost is zero, regardless of the insurer's bargaining power. We further find that the optimality of no insurance is consistent across all market structures. When the insured's risk preference exhibits decreasing absolute risk aversion, the optimal deductible and the insurer's expected loss decrease in the degree of the insured's risk aversion and thus increase in the insured's initial wealth. In addition, the effect of increasing the insurer's bargaining power on the optimal deductible is equivalent to a pure effect of reducing the initial wealth of the insured. Our results suggest that the well-documented preference for low deductibles could be the result of insurance bargaining.

In this paper, under the stochastic interest rate framework, we consider the valuation of a Guaranteed Lifelong Withdrawal Benefit (GLWB) annuity product by explicitly incorporating the health state of the policyholder through the long-term care (LTC) option. The product provides policyholders with protection against longevity risk and market downturns, as well as financial support when facing LTC needs. Within the context of dynamic withdrawals, the valuation of the GLWB annuity with the LTC option is characterized as a stochastic optimal control problem. We introduce a novel bang-bang analysis approach without the usual convexity assumption in literature and prove that the optimal withdrawal strategies for the policyholder are constrained to a finite set. Furthermore, we perform a sensitivity analysis on the price determinants of GLWB annuities with and without the LTC option, and provide economic interpretations. Lastly, we investigate the impact of gender on the optimal withdrawal strategy and the fair fee of the annuity with the LTC option.

This paper studies a general Lévy process model of the bail-out optimal dividend problem with an exponential time horizon, and further extends it to the regime-switching model. We first show the optimality of a double barrier strategy in the single-regime setting with a concave terminal payoff function. This is then applied to show the optimality of a Markov-modulated double barrier strategy in the regime-switching model via contraction mapping arguments. We solve these for a general Lévy model with both positive and negative jumps, greatly generalizing the existing results on spectrally one-sided models.

Decentralized insurance can be used to describe risk sharing mechanisms under which participants trade risks among each other as opposed to passing risks mostly to an insurer in traditional centralized insurance. There are a wide range of decentralized practices in all kinds of forms developed around the world, including online mutual aid in East Asia, takaful in the Middle East, peer-to-peer insurance in the West, international catastrophe risk pooling by African, Caribbean and Central America countries, etc. There is also a rich literature of risk sharing in academia that offers theoretical bases of other decentralized mechanisms. This work presents a unified mathematical framework to describe the commonalities and the relationships of all these seemingly different business in practice and theoretical models in academia. Such a framework provides a fertile ground for the comparison of existing practices and the design and engineering of hybrid and innovative models.

When annuitants' survival probabilities are heterogeneous, the equilibrium annuity price is affected by their annuitization choices, which further depend on the annuity price. Given this mutual dependence, it is generally difficult to establish uniqueness of the equilibrium. Based on similar expressions appearing in several annuity and insurance models, we obtain two results in an annuity model with heterogeneity in survival probability only. First, the equilibrium annuity price is always unique if the annuitization function is multiplicatively separable in survival probability and annuity price. Second, the equilibrium is unique for more general annuitization functions, provided that a sufficient condition on the distribution of survival probabilities holds. Many distributions, including the uniform, normal and gamma distributions, satisfy this condition.

The number and amount of claims, referred to as the sum of claims or the total claim/loss amounts in insurance literature, are crucial pieces of information for insurance companies. The analysis of these numerical values can provide essential insights for targeted planning. This study explores a spatial approach for jointly modeling claim frequency and claim size. We assume that the number of accidents follows a Poisson distribution with a variable mean, and this mean, in turn, has a distribution commonly known as a mixed distribution. The spatial dependence structure within the observations is then modeled using an appropriate copula. By estimating the parameters of the proposed model, we draw prediction maps for both claim frequencies and total claim size. These maps will contribute to the prediction of future claim dynamics, offering insurers the opportunity to refine their market strategies and enhance their overall risk management approach based on evolving spatial patterns.