59 research outputs found
Optimal periodic dividend strategies for spectrally positive L\'evy risk processes with fixed transaction costs
We consider the general class of spectrally positive L\'evy risk processes,
which are appropriate for businesses with continuous expenses and lump sum
gains whose timing and sizes are stochastic. Motivated by the fact that
dividends cannot be paid at any time in real life, we study
dividend strategies whereby dividend decisions are made according to a separate
arrival process.
In this paper, we investigate the impact of fixed transaction costs on the
optimal periodic dividend strategy, and show that a periodic
strategy is optimal when decision times arrive according to an independent
Poisson process. Such a strategy leads to lump sum dividends that bring the
surplus back to as long as it is no less than at a dividend
decision time. The expected present value of dividends (net of transaction
costs) is provided explicitly with the help of scale functions. Results are
illustrated.Comment: Accepted for publication in Insurance: Mathematics and Economic
Optimal Dividends in the Dual Model with Diffusion
In the dual model, the surplus of a company is a Lévy 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 paramete
On the optimality of joint periodic and extraordinary dividend strategies
In this paper, we model the cash surplus (or equity) of a risky business with
a Brownian motion. Owners can take cash out of the surplus in the form of
"dividends", subject to transaction costs. However, if the surplus hits 0 then
ruin occurs and the business cannot operate any more.
We consider two types of dividend distributions: (i) periodic, regular ones
(that is, dividends can be paid only at countable many points in time,
according to a specific arrival process); and (ii) extraordinary dividend
payments that can be made immediately at any time (that is, the dividend
decision time space is continuous and matches that of the surplus process).
Both types of dividends attract proportional transaction costs, and
extraordinary distributions also attracts fixed transaction costs, a realistic
feature. A dividend strategy that involves both types of distributions
(periodic and extraordinary) is qualified as "hybrid".
We determine which strategies (either periodic, immediate, or hybrid) are
optimal, that is, we show which are the strategies that maximise the expected
present value of dividends paid until ruin, net of transaction costs.
Sometimes, a liquidation strategy (which pays out all monies and stops the
process) is optimal. Which strategy is optimal depends on the profitability of
the business, and the level of (proportional and fixed) transaction costs.
Results are illustrated
Stable Dividends under Linear-Quadratic Optimization
The optimization criterion for dividends from a risky business is most often
formalized in terms of the expected present value of future dividends. That
criterion disregards a potential, explicit demand for stability of dividends.
In particular, within actuarial risk theory, maximization of future dividends
have been intensively studied as the so-called de Finetti problem. However,
there the optimal strategies typically become so-called barrier strategies.
These are far from stable and suboptimal affine dividend strategies have
therefore received attention recently. In contrast, in the class of
linear-quadratic problems a demand for stability if explicitly stressed. These
have most often been studied in diffusion models different from the actuarial
risk models. We bridge the gap between these patterns of thinking by deriving
optimal affine dividend strategies under a linear-quadratic criterion for a
general L\'evy process. We characterize the value function by the
Hamilton-Jacobi-Bellman equation, solve it, and compare the objective and the
optimal controls to the classical objective of maximizing expected present
value of future dividends. Thereby we provide a framework within which
stability of dividends from a risky business, as e.g. in classical risk theory,
is explicitly demanded and explicitly obtained
Modelling and understanding count processes through a Markov-modulated non-homogeneous Poisson process framework
The Markov-modulated Poisson process is utilised for count modelling in a
variety of areas such as queueing, reliability, network and insurance claims
analysis. In this paper, we extend the Markov-modulated Poisson process
framework through the introduction of a flexible frequency perturbation
measure. This contribution enables known information of observed event arrivals
to be naturally incorporated in a tractable manner, while the hidden Markov
chain captures the effect of unobservable drivers of the data. In addition to
increases in accuracy and interpretability, this method supplements analysis of
the latent factors. Further, this procedure naturally incorporates data
features such as over-dispersion and autocorrelation. Additional insights can
be generated to assist analysis, including a procedure for iterative model
improvement.
Implementation difficulties are also addressed with a focus on dealing with
large data sets, where latent models are especially advantageous due the large
number of observations facilitating identification of hidden factors. Namely,
computational issues such as numerical underflow and high processing cost arise
in this context and in this paper, we produce procedures to overcome these
problems.
This modelling framework is demonstrated using a large insurance data set to
illustrate theoretical, practical and computational contributions and an
empirical comparison to other count models highlight the advantages of the
proposed approach.Comment: For simulated data sets and code, please go to
https://github.com/agi-lab/reserving-MMNP
SynthETIC: an individual insurance claim simulator with feature control
Recent years have seen rapid increase in the application of machine learning
to insurance loss reserving. They yield most value when applied to large data
sets, such as individual claims, or large claim triangles. In short, they are
likely to be useful in the analysis of any data set whose volume is sufficient
to obscure a naked-eye view of its features. Unfortunately, such large data
sets are in short supply in the actuarial literature. Accordingly, one needs to
turn to synthetic data. Although the ultimate objective of these methods is
application to real data, the use of synthetic data containing features
commonly observed in real data is also to be encouraged.
While there are a number of claims simulators in existence, each valuable
within its own context, the inclusion of a number of desirable (but
complicated) data features requires further development. Accordingly, in this
paper we review those desirable features, and propose a new simulator of
individual claim experience called SynthETIC.
Our simulator is publicly available, open source, and fills a gap in the
non-life actuarial toolkit. The simulator specifically allows for desirable
(but optionally complicated) data features typically occurring in practice,
such as variations in rates of settlements and development patterns; as with
superimposed inflation, and various discontinuities, and also enables various
dependencies between variables. The user has full control of the mechanics of
the evolution of an individual claim. As a result, the complexity of the data
set generated (meaning the level of difficulty of analysis) may be dialled
anywhere from extremely simple to extremely complex
Leprosy in wild chimpanzees
Humans are considered as the main host for Mycobacterium leprae1, the aetiological agent of leprosy, but spillover has occurred to other mammals that are now maintenance hosts, such as nine-banded armadillos and red squirrels2,3. Although naturally acquired leprosy has also been described in captive nonhuman primates4-7, the exact origins of infection remain unclear. Here we describe leprosy-like lesions in two wild populations of western chimpanzees (Pan troglodytes verus) in Cantanhez National Park, Guinea-Bissau and Taï National Park, Côte d'Ivoire, West Africa. Longitudinal monitoring of both populations revealed the progression of disease symptoms compatible with advanced leprosy. Screening of faecal and necropsy samples confirmed the presence of M. leprae as the causative agent at each site and phylogenomic comparisons with other strains from humans and other animals show that the chimpanzee strains belong to different and rare genotypes (4N/O and 2F). These findings suggest that M. leprae may be circulating in more wild animals than suspected, either as a result of exposure to humans or other unknown environmental sources
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