Longevity swaps have been one of the major success stories of pension scheme de-risking in recent years. However, with some few exceptions, all of the transactions to date have been bespoke longevity swaps based upon the mortality experience of a portfolio of named lives. In order for this market to start to meet its true potential, solutions will ultimately be needed that provide protection for all types of members, are cost effective for large and smaller schemes, are tradable, and enable access to the wider capital markets. Index-based solutions have the potential to meet this need; however, concerns remain with these solutions. In particular, the basis risk emerging from the potential mismatch between the underlying forces of mortality for the index reference portfolio and the pension fund/annuity book being hedged is the principal issue that has, to date, prevented many schemes progressing their consideration of index-based solutions. Two-population stochastic mortality models offer an alternative to overcome this obstacle as they allow market participants to compare and project the mortality experience for the reference and target populations and thus assess the amount of demographic basis risk involved in an index-based longevity hedge. In this paper, we systematically assess the suitability of several multi-population stochastic mortality models for assessing basis risks and provide guidelines on how to use these models in practical situations paying particular attention to the data requirements for the appropriate calibration and forecasting of such models.

A new methodology, for optimal customer selection in cross-selling of financial services products, such as mortgage loans and non life insurance contracts, is presented. The optimal cross-sales selection of prospects is such that the expected profit is maximized, while at the same time the risk of suffering future losses is minimized. Expected profit maximization and mean–variance optimization are considered as alternative optimality criteria. In order to solve these optimality problems a stochastic model of the profit, expected to emerge from a single cross-sales prospect and from a selection of prospects, is developed. The related probability distributions of the profit are derived, both for small and large portfolio sizes and in the latter case, asymptotic normality is established. The proposed, profit optimization methodology is thoroughly tested, based on a real data set from a large Swedish insurance company and is shown to achieve considerable profit gains, compared to traditional cross-selling methods, which use only the estimated sales probabilities.

A methodology for pricing of reinsurance contracts in the presence of a catastrophe bond is developed. An important advantage of this approach is that it allows for the pricing of reinsurance contracts consistent with the observed market prices of catastrophe bonds on the same underlying risk process.Within the proposed methodology, an appropriate financial pricing formula is derived, under a market implied risk neutral probability measure for both a catastrophe bond and an aggregate excess of loss reinsurance contract, using a generalised Fourier transform. Efficient numerical methods for the evaluation of this formula, such as the Fast Fourier transform and Fractional Fast Fourier transform, are considered.The methodology is illustrated on several examples including Pareto and Gamma claim severities.

We derive a new, efficient closed-form formula approximating the price of discrete lookback options, whose underlying asset price is driven by an exponential semimartingale process, which includes ( jump) diffusions, Lévy models, affine processes and other models. The derivation of our pricing formula is based on inverting the Fourier transform using B-spline approximation theory. We give an error bound for our formula and establish its fast rate of convergence to the true price. Our method provides lookback option prices across the quantum of strike prices with greater efficiency than for a single strike price under existing methods. We provide an alternative proof to the Spitzer formula for the characteristic function of the maximum of a discretely observed stochastic process, which yields a numerically efficient algorithm based on convolutions. This is an important result which could have a wide range of applications in which the Spitzer formula is utilized. We illustrate the numerical efficiency of our algorithm by applying it in pricing fixed and floating discrete lookback options under Brownian motion, jump diffusion models, and the variance gamma process.

We consider an insurance risk model with extended flexibility, under which claims arrive according to a point process with an order statistics (OS) property, their amounts may have any joint distribution and the premium income is accumulated following any non-decreasing, possibly discontinuous real valued function. We generalize the definition of an OS point process, assuming it is generated by an arbitrary cdf allowing jump discontinuities, which corresponds to an arbitrary (possibly discontinuous) claim arrival cumulative intensity function. The latter feature is appealing for insurance applications since it allows to consider clusters of claims arriving instantaneously. Under these general assumptions, a closed form expression for the joint distribution of the time to ruin and the deficit at ruin is derived, which remarkably involves classical Appell polynomials. Corollaries of our main result generalize previous non-ruin formulas e.g., those obtained by Ignatov and Kaishev (Scand Actuar J 2000(1):46–62, 2000 ; J Appl Probab 41(2):570–578, 2004 ; J Appl Probab 43:535–551, 2006 ) and Lefèvre and Loisel (Methodol Comput Appl Probab 11(3):425–441, 2009 ) for the case of stationary Poisson claim arrivals and by Lefèvre and Picard (Insurance Math Econom 49:512–519, 2011 ; Methodol Comput Appl Probab 16:885–905, 2014 ), for OS claim arrivals.