A generalised property exposure rating framework is presented here to address two issues arising in the standard approach to exposure rating, especially in the context of direct insurance and facultative reinsurance (D&F) property pricing: (a) What to do when the main assumption of exposure rating, scalability – that is, that the probability of a given damage ratio does not depend on the maximum possible

This paper presents analytical representations for an optimal insurance contract under distortion risk measure and in the presence of model uncertainty. We incorporate ambiguity aversion and distortion risk measure through the model of Robert and Therond [(2014) ASTIN Bulletin: The Journal of the IAA, 44(2), 277–302.] as per the framework of Klibanoff et al. [(2005) A smooth model of decision making

Regression modelling involving heavy-tailed response distributions, which have heavier tails than the exponential distribution, has become increasingly popular in many insurance settings including non-life insurance. Mixed Exponential models can be considered as a natural choice for the distribution of heavy-tailed claim sizes since their tails are not exponentially bounded. This paper is concerned

This paper studies deep learning approaches to find optimal reinsurance and dividend strategies for insurance companies. Due to the randomness of the financial ruin time to terminate the control processes, a Markov chain approximation-based iterative deep learning algorithm is developed to study this type of infinite-horizon optimal control problems. The optimal controls are approximated as deep neural

We study the relation between one-year premium risk and ultimate premium risk. In practice, the one-year risk is sometimes related to the ultimate risk by using a so-called emergence pattern formula which postulates a linear relation between both risks. We define the true emergence pattern of the ultimate loss for the one-year premium risk based on a conditional distribution of the ultimate loss derived

In insurance analytics, textual descriptions of claims are often discarded, because traditional empirical analyses require numeric descriptor variables. This paper demonstrates how textual data can be easily used in insurance analytics. Using the concept of word similarities, we illustrate how to extract variables from text and incorporate them into claims analyses using standard generalized linear

We present an actuarial claims reserving technique that takes into account both claim counts and claim amounts. Separate (overdispersed) Poisson models for the claim counts and the claim amounts are combined by a joint embedding into a neural network architecture. As starting point of the neural network calibration, we use exactly these two separate (overdispersed) Poisson models. Such a nested model

Marine is the oldest type of insurance coverage. Nevertheless, unlike cargo and hull covers, marine liability is a rather young line of business with claims that can have very heavy and long tails. For reinsurers, the accumulation of losses from an event insured by various Protection and Indemnity clubs is an additional source for very large claims in the portfolio. In this paper, we first describe

Tontines, retirement products constructed in such a way that the longevity risk is shared in a pool of policyholders, have recently gained vast attention from researchers and practitioners. Typically, these products are cheaper than annuities, but do not provide stable payments to policyholders. This raises the question whether, from the policyholders' viewpoint, the advantages of annuities and tontines

In this paper, we consider the risk–return trade-off for variable annuities in a Black–Scholes setting. Our analysis is based on a novel explicit allocation of initial wealth over the payments at various horizons. We investigate the relationship between the optimal consumption problem and the design of variable annuities by deriving the optimal so-called assumed interest rate for an investor with constant

In this paper, we first derive closed-form formulas for mortality-interest durations and convexities of the prices of life insurance and annuity products with respect to an instantaneously proportional change and an instantaneously parallel movement, respectively, in μ* (the force of mortality-interest), the addition of μ (the force of mortality) and δ (the force of interest). We then build several

We determine the optimal robust strategy of an individual who seeks to maximize the (penalized) probability of reaching a bequest goal when she is uncertain about the drift of the risky asset and her hazard rate of mortality. We assume the individual can invest in a Black–Scholes market. We solve two optimization problems with ambiguity. The first is to maximize the penalized probability of reaching

The existence of long memory in mortality data improves the understandings of features of mortality data and provides a new approach for establishing mortality models. The findings of long-memory phenomena in mortality data motivate us to develop new mortality models by extending the Lee–Carter (LC) model to death counts and incorporating long-memory model structure. Furthermore, there are no identification

A generalization of range-value-at-risk (RVaR) and tail-value-at-risk (TVaR) for d-dimensional distribution functions is introduced. Properties of these new risk measures are studied and illustrated. We provide special cases, applications and a comparison with traditional univariate and multivariate versions of the TVaR and RVaR.

This paper studies bilateral risk sharing under no aggregate uncertainty, where one agent has Expected-Utility preferences and the other agent has Rank-dependent utility preferences with a general probability distortion function. We impose exogenous constraints on the risk exposure for both agents, and we allow for any type or level of belief heterogeneity. We show that Pareto-optimal risk-sharing

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We propose a new inference strategy for general population mortality tables based on annual population and death estimates, completed by monthly birth counts. We rely on a deterministic population dynamics model and establish formulas that link the death rates to be estimated with the observables at hand. The inference algorithm takes the form of a recursive and implicit scheme for computing death

We determine the optimal asset allocation to bonds and stocks using an annually recalculated virtual annuity (ARVA) spending rule for DC pension plan decumulation. Our objective function minimizes downside withdrawal variability for a given fixed value of total expected withdrawals. The optimal asset allocation is found using optimal stochastic control methods. We formulate the strategy as a solution

Variable annuities are products offered by pension funds and life offices that provide periodic future payments to the investor and often have ancillary benefits that guarantee survival benefits or sums insured on death. This paper extends the benchmark approach to value and hedge long-dated variable annuities using a combination of cash, bonds and equities under a variety of market models, allowing

We study a weighted comonotonic risk-sharing problem among multiple agents with distortion risk measures under heterogeneous beliefs. The explicit forms of optimal allocations are obtained, which are Pareto-optimal. A necessary and sufficient condition is given to ensure the uniqueness of the optimal allocation, and sufficient conditions are given to obtain an optimal allocation of the form of excess

When modelling subnational mortality rates, we should consider three features: (1) how to incorporate any possible correlation among subpopulations to potentially improve forecast accuracy through multi-population joint modelling; (2) how to reconcile subnational mortality forecasts so that they aggregate adequately across various levels of a group structure; (3) among the forecast reconciliation methods

This paper provides a toolbox for the credibility analysis of frequency risks, with allowance for the seniority of claims and of risk exposure. We use Poisson models with dynamic and second-order stationary random effects that ensure nonnegative credibilities per period. We specify classes of autocovariance functions that are compatible with positive random effects and that entail nonnegative credibilities