On the optimal dividend problem for a spectrally negative L\'{e}vy process

In this paper we consider the optimal dividend problem for an insurance company whose risk process evolves as a spectrally negative L\'{e}vy process in the absence of dividend payments. The classical dividend problem for an insurance company consists in finding a dividend payment policy that maximizes the total expected discounted dividends. Related is the problem where we impose the restriction that ruin be prevented: the beneficiaries of the dividends must then keep the insurance company solvent by bail-out loans. Drawing on the fluctuation theory of spectrally negative L\'{e}vy processes we give an explicit analytical description of the optimal strategy in the set of barrier strategies and the corresponding value function, for either of the problems. Subsequently we investigate when the dividend policy that is optimal among all admissible ones takes the form of a barrier strategy.Comment: Published at http://dx.doi.org/10.1214/105051606000000709 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Exit problem of a two-dimensional risk process from the quadrant: Exact and asymptotic results

Consider two insurance companies (or two branches of the same company) that divide between them both claims and premia in some specified proportions. We model the occurrence of claims according to a renewal process. One ruin problem considered is that of the corresponding two-dimensional risk process first leaving the positive quadrant; another is that of entering the negative quadrant. When the claims arrive according to a Poisson process, we obtain a closed form expression for the ultimate ruin probability. In the general case, we analyze the asymptotics of the ruin probability when the initial reserves of both companies tend to infinity under a Cram\'{e}r light-tail assumption on the claim size distribution.Comment: Published in at http://dx.doi.org/10.1214/08-AAP529 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

On Gerber-Shiu functions and optimal dividend distribution for a L\'{e}vy risk process in the presence of a penalty function

This paper concerns an optimal dividend distribution problem for an insurance company whose risk process evolves as a spectrally negative L\'{e}vy process (in the absence of dividend payments). The management of the company is assumed to control timing and size of dividend payments. The objective is to maximize the sum of the expected cumulative discounted dividend payments received until the moment of ruin and a penalty payment at the moment of ruin, which is an increasing function of the size of the shortfall at ruin; in addition, there may be a fixed cost for taking out dividends. A complete solution is presented to the corresponding stochastic control problem. It is established that the value-function is the unique stochastic solution and the pointwise smallest stochastic supersolution of the associated HJB equation. Furthermore, a necessary and sufficient condition is identified for optimality of a single dividend-band strategy, in terms of a particular Gerber-Shiu function. A number of concrete examples are analyzed.Comment: Published at http://dx.doi.org/10.1214/14-AAP1038 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Bankruptcy risk forecasting for the metallurgical branch in Romania

All investment decisions require a thorough analysis of the retrospective evolution of the entities from the concerned area, in order to estimate the long-term evolution perspectives. In this context, the present study analyzes the evolution of the entities from the Romanian metallurgical sector based on the accounting and financial information published for the period 2008 - 2012 and, in fact, it justifies the situation from the perspective of users (managers, investors, auditors) and of the economic environment specific to Romania. Starting from this premise we created a regression model particularly useful in forecasting the evolution of the ability to deal with debt for the entities from the Romanian metallurgical sector

Determinant factors for the growing of shareholders’ equity in the metallurgical sector in Romania

The article provides a statistical monograph of the financial position and performance for the period 2008 – 2012 of the entities from the Romanian metallurgical sector whose financial statements in the period 2004 – 2012 have become the object of the financial audit. There are tested five types of regression models in order to separately determine the evolution of equity in accordance with the variation of turnover, total assets, average number of employees and net result. After determining the most appropriate simple regression model, one proceeds at establishing a multiple regression model which would simultaneously reflect the evolution of equity in accordance with the above mentioned variables. The study’s importance is enhanced by certain statistically-based concrete measures which management should consider in order to increase the shareholders’ equity

Dynamics of an SIR epidemic model with limited medical resources, revisited and corrected

This paper generalizes and corrects a famous paper (more than 200 citations) concerning Hopf and Bogdanov-Takens bifurcations due to L. Zhou and M. Fan, "Dynamics of an SIR epidemic model with limited medical resources revisited", in which we discovered a significant numerical error. Importantly, unlike the paper of Zhou and Fan and several other papers that followed them, we offer a notebook where the reader may recover all the results and modify them for analyzing similar models. Our calculations lead to the introduction of some interesting symbolic objects, "Groebner eliminated traces and determinants" - see (4.5), (4.6), which seem to have appeared here for the first time and which might be of independent interest. We hope our paper might serve as yet another alarm bell regarding the importance of accompanying papers involving complicated hand computations by electronic notebooks

Pluralism About Group Knowledge: A Reply to Jesper Kallestrup

Jesper Kallestrup has provided an insightful response to our paper, “Epistemic Structure in Non-Summative Social Knowledge”. Kallestrup identifies some important issues pertaining to our non-summative, non-supervenient account of group knowledge which we did not address in our original paper. Here, we develop our view further in light of Kallestrup’s helpful reply

Identifying Patient Candidates for IL-1 Inhibition: Lessons From Real-World Cases

A subgroup of patients with gouty arthritis have a chronic recurring form that is particularly difficult to treat. Such patients experience repeated flares and often have abundant tophi. Many also have underlying comorbidities, such as renal impairment, cardiovascular disease, gastrointestinal disorders, obesity, and hypertension, which contraindicate the use of standard anti-inflammatory medications. Five patients with difficult to treat gouty arthritis who were either candidates and/or treated with anti-IL therapy are described.info:eu-repo/semantics/publishedVersio