Risks, Volume 4, Issue 1 (March 2016) – 8 articles

In the classical expected utility framework, a problem of optimal insurance design with a premium constraint is equivalent to a problem of optimal insurance design with a minimum expected retention constraint. When the insurer has ambiguous beliefs represented by a non-additive probability measure, as in Schmeidler, this equivalence no longer holds. Recently, Amarante, Ghossoub and Phelps examined the problem of optimal insurance design with a premium constraint when the insurer has ambiguous beliefs. In particular, they showed that when the insurer is ambiguity-seeking, with a concave distortion of the insured’s probability measure, then the optimal indemnity schedule is a state-contingent deductible schedule, in which the deductible depends on the state of the world only through the insurer’s distortion function. In this paper, we examine the problem of optimal insurance design with a minimum expected retention constraint, in the case where the insurer is ambiguity-seeking. We obtain the aforementioned result of Amarante, Ghossoub and Phelps and the classical result of Arrow as special cases. Full article

This paper features an analysis of major currency exchange rate movements in relation to the US dollar, as constituted in US dollar terms. Euro, British pound, Chinese yuan, and Japanese yen are modelled using a variety of non-linear models, including smooth transition regression models, logistic smooth transition regressions models, threshold autoregressive models, nonlinear autoregressive models, and additive nonlinear autoregressive models, plus Neural Network models. The models are evaluated on the basis of error metrics for twenty day out-of-sample forecasts using the mean average percentage errors (MAPE). The results suggest that there is no dominating class of time series models, and the different currency pairs relationships with the US dollar are captured best by neural net regression models, over the ten year sample of daily exchange rate returns data, from August 2005 to August 2015. Full article

This paper proposes a model for the claim occurrence, reporting, and handling process of insurance companies. It is assumed that insurance claims occur according to a Markovian arrival process. An incurred claim goes through some stages of a claim reporting and handling process, such as Incurred But Not Reported (IBNR), Reported But Not Settled (RBNS) and Settled (S). We derive formulas for the joint distribution and the joint moments for the amount of INBR, RBNS and Settled claims. This model generalizes previous ones in the literature, which generally assume Poisson claim arrivals. Due to the flexibility of the Markovian arrival process, the model can be used to evaluate how the claim occurring, reporting, and handling mechanisms may affect the volatilities of the amount of IBNR, RBNS and Settled claims, and the interdependencies among them. Full article

In insurance and related industries including healthcare, it is common to have several outcome measures that the analyst wishes to understand using explanatory variables. For example, in automobile insurance, an accident may result in payments for damage to one’s own vehicle, damage to another party’s vehicle, or personal injury. It is also common to be interested in the frequency of accidents in addition to the severity of the claim amounts. This paper synthesizes and extends the literature on multivariate frequency-severity regression modeling with a focus on insurance industry applications. Regression models for understanding the distribution of each outcome continue to be developed yet there now exists a solid body of literature for the marginal outcomes. This paper contributes to this body of literature by focusing on the use of a copula for modeling the dependence among these outcomes; a major advantage of this tool is that it preserves the body of work established for marginal models. We illustrate this approach using data from the Wisconsin Local Government Property Insurance Fund. This fund offers insurance protection for (i) property; (ii) motor vehicle; and (iii) contractors’ equipment claims. In addition to several claim types and frequency-severity components, outcomes can be further categorized by time and space, requiring complex dependency modeling. We find significant dependencies for these data; specifically, we find that dependencies among lines are stronger than the dependencies between the frequency and average severity within each line. Full article

Long-term care insurance (LTCI) covers are rather recent products, in the framework of health insurance. It follows that specific biometric data are scanty; pricing and reserving problems then arise because of difficulties in the choice of appropriate technical bases. Different benefit structures imply different sensitivity degrees with respect to changes in biometric assumptions. Hence, an accurate sensitivity analysis can help in designing LTCI products and, in particular, in comparing stand-alone products to combined products, i.e., packages including LTCI benefits and other lifetime-related benefits. Numerical examples show, in particular, that the stand-alone cover is much riskier than all of the LTCI combined products that we have considered. As a consequence, the LTCI stand-alone cover is a highly “absorbing” product as regards capital requirements for solvency purposes. Full article

We consider a discrete-time dependent Sparre Andersen risk model which incorporates multiple threshold levels characterizing an insurer’s minimal capital requirement, dividend paying situations, and external financial activities. We focus on the development of a recursive computational procedure to calculate the finite-time ruin probabilities and expected total discounted dividends paid prior to ruin associated with this model. We investigate several numerical examples and make some observations concerning the impact our threshold levels have on the finite-time ruin probabilities and expected total discounted dividends paid prior to ruin. Full article