Benjamin Avanzi

Strategies for Dividend Distribution: A Review

Abstract In today’s world of financial uncertainty, one major public concern is to assess (and possibly improve) the stability of companies that take on risks. Actuaries have been aware of that issue for a very long time and have a great experience in modeling the activity of a risk business. During the first part of the twentieth century, they focused on the probability of ruin to assess the stability of their company. In his seminal paper of 1957 Bruno de Finetti criticized this approach and laid the foundations of what would become an increasingly popular topic: the study of dividend strategies. The contributions made by actuaries in that field constitute a substantial body of knowledge, whose interest is relevant not only to insurance but also to a much broader range of areas of practice. In this paper we aim at a taxonomical synthesis of the 50 years of actuarial research that followed de Finetti’s original paper.

Optimal Dividends in the Dual Model with Diffusion

In the dual model, the surplus of a company is a Levy process with sample paths that are skip-free downwards. In this paper, the aggregate gains process is the sum of a shifted compound Poisson process and an independent Wiener process. By means of Laplace transforms, it is shown how the expectation of the discounted dividends until ruin can be calculated, if a barrier strategy is applied, and how the optimal dividend barrier can be determined. Conditions for optimality are discussed and several numerical illustrations are given. Furthermore, a family of models is analysed where the individual gain amount distribution is rescaled and compensated by a change of the Poisson parameter.

On Optimal Periodic Dividend Strategies in the Dual Model with Diffusion

The dual model with diffusion is appropriate for companies with continuous expenses that are offset by stochastic and irregular gains. Examples include research-based or commission-based companies. In this context, Bayraktar et al. (2013a) show that a dividend barrier strategy is optimal when dividend decisions are made continuously. In practice, however, companies that are capable of issuing dividends make dividend decisions on a periodic (rather than continuous) basis.

What is it that Makes the Swiss Annuitise? A Description of the Swiss Retirement System

The Swiss model of retirement savings and benefits distinguishes itself in several aspects. The system is successful in encouraging substantial savings, which are exonerated from tax and guaranteed. The associated market risk is not transferred to the individuals. From an international perspective it is extraordinary that more than half of the Swiss who retire choose to annuitise their capital at retirement. In addition, not only does the retirement scheme offer annuity benefits at retirement, but it also offers annuity benefits on disability and death. In this paper we describe the Swiss social security system with an emphasis on retirement benefits, giving some insights as to what in Switzerland could explain why the so-called annuity puzzle is not observed. We also discuss some of the main issues the Swiss pensions system is currently facing.

Real Options at the Interface of Finance and Operations: Exploiting Embedded Supply Chain Real Options to Gain Competitiveness

Exploiting embedded supply-chain real options creates powerful opportunities for competitive manufacturing in high-cost environments. Rather than seeking competitiveness through standardization as is common to lean production, real-options reasoning explores opportunities to use supply-chain variability as a strategic weapon. We present an illustrative case study of a Swiss manufacturer of cable extrusion equipment supported by a formal real-options model that aids in valuing the embedded options that make up supply-chain flexibility: postponement, contraction, expansion, switching, and abandonment. Real-options reasoning provides a plausible retrospective rationale for the case firms use of supply-chain flexibility that provided protection against competition from low cost, but less responsive competitors. Their intuitive real-options reasoning facilitated incorporating fuller information concerning volatility, flexibility, and control into choosing what products to make, in what quantity, and with work allocated to which supplier. The case study also highlights how competing through exploiting embedded real options requires a different managerial skill set than does competing through cost reduction. Skills such as customer communication, supplier management, and ability to ensure a smooth flow of production join the ability to reduce and control lead times as key sources of competitive advantage.

Modelling Dependence in Insurance Claims Processes with Lévy Copulas

In this paper we investigate the potential of Levy copulas as a tool for modelling dependence between compound Poisson processes and their applications in insurance. We analyse characteristics regarding the dependence in frequency and dependence in severity allowed by various Levy copula models. Through the

Stochastic Loss Reserving with Dependence: A Flexible Multivariate Tweedie Approach

Stochastic loss reserving with dependence has received increased attention in the last decade. A number of parametric multivariate approaches have been developed to capture dependence between lines of business within an insurers portfolio. Motivated by the richness of the Tweedie family of distributions, we propose a multivariate Tweedie approach to capture cell-wise dependence in loss reserving. This approach provides a transparent introduction of dependence through a common shock structure. In addition, it also has a number of ideal properties, including marginal flexibility, transparency, and tractability including moments that can be obtained in closed form. Theoretical results are illustrated using a simulated data set and a real data set from a property-casualty insurer in the US.

A Note on Realistic Dividends in Actuarial Surplus Models

Because of the profitable nature of risk businesses in the long term, de Finetti suggested that surplus models should allow for cash leakages, as otherwise the surplus would unrealistically grow (on average) to infinity. These leakages were interpreted as ‘dividends’. Subsequent literature on actuarial surplus models with dividend distribution has mainly focussed on dividend strategies that either maximise the expected present value of dividends until ruin or lead to a probability of ruin that is less than one (see Albrecher and Thonhauser, Avanzi for reviews). An increasing number of papers are directly interested in modelling dividend policies that are consistent with actual practice in financial markets. In this short note, we review the corporate finance literature with the specific aim of fleshing out properties that dividend strategies should ideally satisfy, if one wants to model behaviour that is consistent with practice.

Capturing Non-Exchangeable Dependence in Multivariate Loss Processes with Nested Archimedean Lévy Copulas

The class of spectrally positive Lévy processes is a frequent choice for modelling loss processes in areas such as insurance or operational risk. Dependence between such processes (for example, between different lines of business) can be modelled with Lévy copulas. This approach is a parsimonious, efficient, and flexible method which provides many of the advantages akin to distributional copulas for random variables. Literature on Lévy copulas seems to have primarily focused on bivariate processes. When multivariate settings are considered, these usually exhibit an exchangeable dependence structure (whereby all subset of the processes have an identical marginal Lévy copula). In reality, losses are not always associated in an identical way, and models allowing for non-exchangeable dependence patterns are needed. In this paper, we present an approach which enables the development of such models. Inspired by ideas and techniques from the distributional copula literature we investigate the procedure of nesting Archimedean Lévy copulas. We provide a detailed analysis of this construction, and derive conditions under which valid multivariate (nested) Lévy copulas are obtained. Our results are discussed and illustrated, notably with an example of model fitting to data.

Common Shock Models for Claim Arrays

The paper is concerned with multiple claim arrays. We construct a broad and flexible family of models, where dependency is induced by common shock components. Models incorporate dependencies between observations both within arrays and between arrays. Arrays are of general shape (possibly with holes), but include the usual cases of claim triangles and trapezia that appear in the literature. General forms of dependency are considered, with cell-, row-, column-, diagonal-wise, and other, forms of dependency as special cases. In recognition of the extensive use by practitioners of large correlation matrices for the estimation of diversification benefits in capital modelling, substantial effort is applied to practical interpretation of such matrices generated by the models constructed here. Indeed, the literature does not document any methodology by which practitioners, who often parametrise those correlations by means of informed guesswork, may do so in a disciplined and parsimonious manner. In fact, this motivated the work presented in this paper.Reasonably realistic examples are examined, in which an expression is obtained for the general entry in the correlation matrix in terms of a limited set of parameters, each of which has a straightforward intuitive meaning to the practitioner. This will maximise chance of obtaining a reliable matrix. This construction is illustrated by a numerical example. Finally, the generated correlation matrix is then combined with heuristic estimates of tail dependency to arrive at a t-copula which might be used to construct capital margins dealing with the extreme right tail.