Insurance Mathematics & Economics最新文献

We provide new results about the comparative static effects of income risk and interest rate risk on optimal risk-reduction and saving decisions. We combine arguments from the risk apportionment literature with monotone comparative statics. Risk reduction and saving are Edgeworth-Pareto substitutes for (mixed) risk averters and Edgeworth-Pareto complements for (mixed) risk lovers. For changes in income risk, risk reduction and saving are Nth-degree risk complements for risk lovers. For changes in interest rate risk, risk reduction and saving are Nth-degree risk substitutes for risk averters. The individual's risk attitude and the source of risk thus co-determine the effects of risk changes on optimal. We also discuss several extensions including multiple loss states, higher-order risk reduction, stochastic dominance, non-separable utility, and inflation risk.

We propose a ‘buy, hold, sell’ (BHS) deterministic lifecycle strategy that involves buying and holding assets until they are sold to generate income. Savings are invested entirely into a risky portfolio until a pre-specified ‘switch age’ and then entirely into a risk-free portfolio after the switch age, followed by withdrawing during the payout phase from both portfolios based on annuitization factors that vary with age. We also allow for access to mortality credits through an insurance market. We analytically derive the dynamics of the investment strategy and show that the strategy is optimal for a range of investors with HARA risk preferences. We demonstrate numerically that the BHS strategy delivers limited loss of utility versus an optimal solution for investors with CRRA preferences and low-moderate levels of risk aversion while significantly outperforming deterministic strategies commonly seen in practice. The BHS strategy offers an attractive alternative for practical applications as it is straightforward to apply while avoiding the need for dynamic optimization and portfolio rebalancing.

By exploiting massive amounts of data, machine learning techniques provide actuaries with predictors exhibiting high correlation with claim frequencies and severities. However, these predictors generally fail to achieve financial equilibrium and thus do not qualify as pure premiums. Autocalibration effectively addresses this issue since it ensures that every group of policyholders paying the same premium is on average self-financing. Balance correction has been proposed as a way to make any candidate premium autocalibrated with the added advantage that it improves out-of-sample Bregman divergence and hence predictive Tweedie deviance. This paper proves that balance correction is also beneficial in terms of concentration curves and derives conditions ensuring that the initial predictor and its balance-corrected version are ordered in Lorenz order. Finally, criteria are proposed to rank the balance-corrected versions of two competing predictors in the convex order.

This paper introduces an extension of stochastic dominance, moving from univariate to bivariate analysis by incorporating a reference function. Our approach offers flexibility in reference function selection, improving upon previous studies cohesively. Bivariate orderings are invaluable tools in actuarial sciences, facilitating the assessment and management of dependencies between risks and lifelengths within multiple insurance contracts. These advancements hold promising practical implications, particularly within the actuarial sciences domain.

We introduce a new stochastic order for the tail dependence between random variables. We then study different measures of tail dependence which are monotone in the proposed order, thereby extending various known tail dependence coefficients from the literature. We apply our concepts in an empirical study where we investigate the tail dependence for different pairs of S&P 500 stocks and indices, and illustrate the advantage of our measures of tail dependence over the classical tail dependence coefficient.

We study risk processes with level dependent premium rate. Assuming that the premium rate converges, as the risk reserve increases, to the critical value in the net-profit condition, we obtain upper and lower bounds for the ruin probability; our proving technique is purely probabilistic and based on the analysis of Markov chains with asymptotically zero drift.

We show that such risk processes give rise to heavy-tailed ruin probabilities whatever the distribution of the claim size, even if it is a bounded random variable. So, the risk processes with near critical premium rate provide an important example of a stochastic model where light-tailed input produces heavy-tailed output.

Relative spillover effects play a crucial role in the analysis and comparison of systemic risks. This paper introduces a novel approach, referred to as distortion risk contribution ratio measures, for quantifying such effects. Various types of contribution ratio measures are defined based on the newly proposed conditional distortion risk measures by Dhaene et al. (2022), and useful integral-based representations are provided as well. An interesting equivalent characterization result for the convex transform order is also presented, which is not only relevant to proving our main results but also has independent value in other research areas. We then establish comparison results between the distortion risk contribution ratio measures of two different bivariate random vectors with either the same or different copulas. Sufficient conditions are established in terms of stochastic orders, copula functions, distortion functions, and stress levels. Furthermore, we investigate the ordering behaviors of these measures in relation to the interaction between paired risks. Numerical examples are presented to illustrate the conditions and main findings.

A functional defined on random variables f is law invariant with respect to a reference probability if its value only depends on the distribution of its argument f under that measure. In contrast to most of the literature on the topic, we take a concrete functional as given and ask if there can be more than one such reference probability. For wide classes of functionals – including, for instance, monetary risk measures and return risk measures – we demonstrate that this is not the case unless they are (i) constant, or (ii) more generally depend only on the essential infimum and essential supremum of the argument f. Mathematically, the results leverage Lyapunov's Convexity Theorem.

Guaranteed Lifetime Withdrawal Benefits (GLWBs) are an increasingly popular add-on to Variable Annuities, offering a guaranteed stream of payments for the remainder of the policyholder's life. GLWBs have typically been priced using numerical methods such as finite difference schemes or Monte Carlo simulations; obtaining accurate and precise solutions using these methods can be very computationally expensive. In this paper, we extend an existing method for analytic pricing of these policies to a more general fee structure. We introduce a novel variation on the commonly offered ratchet rider that more directly addresses policyholder motivation around lapse-and-reentry behaviour. We then modify our pricing method to accommodate this new rider and compare it to the existing annual ratchet with respect to a policyholder's incentive to lapse such a policy.

Lifetime pension pools—also known as group self-annuitization plans, pooled annuity funds, and retirement tontines in the literature—allow retirees to convert a lump sum into lifelong income, with payouts linked to investment performance and the collective mortality experience of the pool. Existing literature on these pools has predominantly examined basic investment strategies like constant allocations and investments solely in risk-free assets. Recent studies, however, proposed volatility targeting, aiming to enhance risk-adjusted returns and minimize downside risk. Yet they only considered investment risk in the volatility target, neglecting the impact of mortality risk on the strategy. This study thus aims to address this gap by investigating volatility-targeting strategies for both investment and mortality risks, offering a solution that keeps the risk associated with benefit variation as constant as possible through time. Specifically, we derive a new asset allocation strategy that targets both investment and mortality risks, and we provide insights about it. Practical investigations of the strategy demonstrate the effectiveness and robustness of the new dynamic volatility-targeting approach, ultimately leading to enhanced lifetime pension benefits.