We consider the pricing of American-type basket derivatives by numerically solving a partial differential equation (PDE). The curse of dimensionality inherent to basket derivative pricing is circumvented by using the theory of comonotonicity. We start with deriving a PDE for the Europeantype comonotonic basket derivative price, together with a unique self-financing hedging strategy. We show how to use the results for the comonotonic market to approximate American-type basket derivative prices for a basket with correlated stocks. Our methodology generates American basket option prices which are in line with the prices obtained via the standard Least-Square Monte Carlo approach. Moreover, the numerical tests illustrate the performance of the proposed method in terms of computation time, and highlight some deficiencies of the standard LSM method.

This paper considers the problem of a lifelong health insurance cover where medical inflation is not sufficiently incorporated in the level premium determined at policy issue. We focus on the setting where changes in health benefits, driven by medical inflation, are accounted for by an appropriate update or indexation of the level premium, the policy value, or both premium and policy value, during the term of the contract. Such an updating mechanism is necessary to restore the actuarial equivalence between future health benefits and surrender values on the one hand, and available policy values and future premiums on the other hand. We extend existing literature (Vercruysse et al., 2013; Denuit et al., 2017) by developing updating mechanisms in a discrete-time framework, where medical inflation is only taken into account ex-post as it emerges over time and where surrender values are allowed for. We propose and design two types of surrender values: based on the ageing provision on the one hand and based directly on the premiums paid until surrender on the other hand. We illustrate our updating strategy with numerical examples, using Belgian data, and investigate the sensitivity of our findings with respect to elements from the technical basis (in particular: the lapse rates) used in the actuarial calculations. Our updating mechanism is generic and useful for a wide range of products in life and health insurance, where some elements of the technical basis are guaranteed while others are subject to revision according to policy conditions.

This paper proposes a practical way for ex-post indexing of level premiums in lifelong medical insurance contracts, in order to take into account observed medical inflation. The We show that ex-post indexing can be achieved by considering only premiums, without explicit reference to reserves. This appears to be relevant in practice as reserving mechanisms may not be transparent to policyholders and as some mutual and shareholder insurers do not compute contract-specific reserves, managing the whole portfolio in a collective way. Note that the similarity with the existing literature on life insurance comes from the lifelong nature of the contracts considered in our setting. However, in the case of health insurance covers the value of future benefits is random. The present study originates from a proposal for indexing lifelong medical insurance level premiums in Belgium. As an application, we study the impact of various indexing mechanisms on a typical medical insurance portfolio on the Belgian market.

This paper proposes a practical way for ex-post indexing of level premiums in lifelong medical insurance contracts, in order to take into account observed medical inflation. The We show that ex-post indexing can be achieved by considering only premiums, without explicit reference to reserves. This appears to be relevant in practice as reserving mechanisms may not be transparent to policyholders and as some mutual and shareholder insurers do not compute contract-specific reserves, managing the whole portfolio in a collective way. Note that the similarity with the existing literature on life insurance comes from the lifelong nature of the contracts considered in our setting. However, in the case of health insurance covers the value of future benefits is random. The present study originates from a proposal for indexing lifelong medical insurance level premiums in Belgium. As an application, we study the impact of various indexing mechanisms on a typical medical insurance portfolio on the Belgian market.

This paper addresses systematic longevity risk in long-term insurance business. We analyze the consequences of working under unknown survival probabilities on the efficiency of the Law of Large Numbers and point out the need for appropriate and feasible risk management techniques. We propose a general setting for risk sharing schemes between the insurer and policyholders via a dynamic equivalence principle. We focus on a pure endowment contract and derive conditions for a viable risk sharing scheme which enhances the solvency situation of the insurer while being attractive to the clients.