The Bismarck Era

This chapter examines German-Russian relations during the Bismarck era (1871-90). The bulk of the chapter draws on the primary and secondary historical record to evaluate how key German and Russian decision makers thought about each other’s intentions in the periods before and after the formation of the First Dreikaiserbund, the Congress of Berlin, the creation of the Second Dreikaiserbund, and the making of the Reinsurance Treaty. Were they confident that their counterparts had benign intentions—that is, did they trust each other—as asserted by intentions optimists? Or were they uncertain about each other’s intentions, which is to say that they mistrusted each other, as suggested by intentions pessimism? Having shown that Berlin and St. Petersburg were far from confident that the other side had benign intentions throughout the Bismarck era, the chapter concludes by describing the shape of the resulting German-Russian security competition.

On the Reasons Why the Reinsurance Treaty Was not Renewed in 1890

The article is aimed at discussing the reasons for the non-renewal of the Reinsurance Treaty in 1890 between Russia and Germany. It analyses the fundamental traits of Bismarck’s foreign policy towards Russia and subsequently deals with the impact of Bismarck’s resignation. It further details the shift in attitudes towards Russia by Bismarck’s replacement in order to understand why the Treaty was not renewed. The article also determines how this shift influenced international politics and lists the reasons for French and Russian relations growing. The study uses methodological approaches of “traditional” political history, meaning history of states and diplomacy based on “the primacy of foreign policy” and research fields aimed at actions of states and their highest political representatives. Based on the methodological approaches, an analysis has been conducted of “highest policy” and a “realistic” insight into the history of foreign policy is presented in narrative form. The author agrees with the opinion that the changes in German foreign policy led to the so-called “revolution of the alliances”. Based on unpublished sources found during archival research, the study concludes that the post-Bismarck diplomacy negatively impacted Germany’s international position since its actions brought France and Russia closer and left Germany with the weakest ally, i.e. Austria-Hungary. The study further concludes that these changes symbolized a huge loss for Germany’s diplomacy. The author assesses that the new diplomacy did not prove itself, calculated falsely, analyzed incorrectly, and predicted wrongly.

Application of Convex Optimization Results of De Finetti's problem for Proportional Reinsurance (Study case CAARAMA insurance campany in Algiers)

The objective of this research is to find the optimal retention level for a proportional reinsurance treaty based on the results of the convex optimization developed in De Finetti’s model. The latter makes it possible to determine the level of retention that achieves the expected profit by the insurer, while minimizing claims volatility. The convex functions appear abundantly in economics and finance. They have remarkable specificities that allows actuaries to minimize financial risks to which some institutions are exposed, especially insurance companies. Therefore, the use of mathematical tools to manage the various risks is paramount.In order to remedy the optimization problem, we have combined the probability of failure method with the "De Finetti" model for proportional reinsurance, which proposed a retention optimization process that minimizes claim volatility for a fixed expected profit based on the results of the non-linear optimization. JEL Codes: C02, C25, C61, G22.

Loss portfolio transfer treaties within Solvency II capital system: a reinsurer’s point of view

Loss portfolio transfer (LPT) is a reinsurance treaty in which an insurer cedes the policies that have already incurred losses to a reinsurer. This operation can be carried out by an insurance company in order to reduce reserving risk and consequently reduce its capital requirement calculated, according to Solvency II. From the viewpoint of the reinsurance company, being a very complex operation, importance must be given to the methodology used to determine the price of the treaty.Following the collective risk approach, the paper examines the risk profiles and the reinsurance pricing of LPT treaties, taking into account the insurance capital requirements established by European law. For this purpose, it is essential to calculate the capital need for the risk deriving from the LPT transaction. In the case analyzed, this requirement is calculated under Solvency II legislation, considering the measure of variability determined via simulation. This quantification was also carried out for different levels of the cost of capital rate, providing a range of possible loadings to be applied to the premium. In the case of the Cost of Capital (CoC) approach, the results obtained provide a lower level of premium compared to the percentile-based method with a range between 2.69% and 1.88%. Besides, the CoC approach also provides the advantage of having an explicit parameter, the CoC rate whose specific level can be chosen by the reinsurance company based on the risk appetite.

Optimal Layer Reinsurance for Compound Fractional Poisson Model

In this paper, we study the optimal retentions for an insurer with a compound fractional Poisson surplus and a layer reinsurance treaty. Under the criterion of maximizing the adjustment coefficient, the closed form expressions of the optimal results are obtained. It is demonstrated that the optimal retention vector and the maximal adjustment coefficient are not only closely related to the parameter of the fractional Poisson process, but also dependent on the time and the claim intensity, which is different from the case in the classical compound Poisson process. Numerical examples are presented to show the impacts of the three parameters on the optimal results.

AN INCLUSIVE CRITERION FOR AN OPTIMAL CHOICE OF REINSURANCE

In this paper, we propose an inclusive model which allows to improve the results obtained in the literature with regard to the criteria set by the insurers such as, maximizing the expected technical benefit under the variance constraint (mean-variance), minimizing the probability of ruin and minimizing risk measures. In this model, we determine the optimal reinsurance treaty parameter that minimizes both the risk and the probability of ruin (by maximizing the Lundberg adjustment coefficient) under the constraint of the technical benefit which must also be maximal, based on the conditional tail variance (CTV) risk measure. Thus, we have developed an optimization procedure based on the augmented Lagrangian and genetic algorithms, in order to solve the optimization program of this model.

A NEYMAN-PEARSON PERSPECTIVE ON OPTIMAL REINSURANCE WITH CONSTRAINTS

The formulation of optimal reinsurance policies that take various practical constraints into account is a problem commonly encountered by practitioners. In the context of a distortion-risk-measure-based optimal reinsurance model without moral hazard, this article introduces and employs a variation of the Neyman–Pearson Lemma in statistical hypothesis testing theory to solve a wide class of constrained optimal reinsurance problems analytically and expeditiously. Such a Neyman–Pearson approach identifies the unit-valued derivative of each ceded loss function as the test function of an appropriate hypothesis test and transforms the problem of designing optimal reinsurance contracts to one that resembles the search of optimal test functions achieved by the classical Neyman–Pearson Lemma. As an illustration of the versatility and superiority of the proposed Neyman–Pearson formulation, we provide complete and transparent solutions of several specific constrained optimal reinsurance problems, many of which were only partially solved in the literature by substantially more difficult means and under extraneous technical assumptions. Examples of such problems include the construction of the optimal reinsurance treaties in the presence of premium budget constraints, counterparty risk constraints and the optimal insurer–reinsurer symbiotic reinsurance treaty considered recently in Cai et al. (2016).

OPTIMAL REINSURANCE WITH LIMITED CEDED RISK: A STOCHASTIC DOMINANCE APPROACH

An optimal reinsurance problem from the perspective of an insurer is studied in this paper, where an upper limit is imposed on a reinsurer's expected loss over a prescribed level. In order to reduce the moral hazard, we assume that both the insurer and the reinsurer are obligated to pay more as the amount of loss increases in a typical reinsurance treaty. We further assume that the optimization criterion preserves the convex order. Such a criterion is very general as most of the criteria for optimal reinsurance problems in the literature preserve the convex order. When the reinsurance premium is calculated as a function of the actuarial value of coverage, we show via a stochastic dominance approach that any admissible reinsurance policy is dominated by a stop-loss reinsurance or a two-layer reinsurance, depending upon the amount of the reinsurance premium. Moreover, we obtain a similar result to Mossin's Theorem and find that it is optimal for the insurer to cede a loss as much as possible under the net premium principle. To further examine the reinsurance premium for the optimal piecewise linear reinsurance policy, we assume the expected value premium principle and derive the optimal reinsurance explicitly under (1) the criterion of minimizing the variance of the insurer's risk exposure, and (2) the criterion of minimizing the risk-adjusted value of the insurer's liability where the liability valuation is carried out using the cost-of-capital approach based on the conditional value at risk.