scholarly journals Risk aggregation and capital allocation using a new generalized Archimedean copula

2022 ◽  
Vol 102 ◽  
pp. 75-90
Author(s):  
Fouad Marri ◽  
Khouzeima Moutanabbir
Author(s):  
Joachim Paulusch

The core of risk aggregation in the Solvency II Standard Formula is the so-called square root formula. We argue that it should be seen as a means for the aggregation of different risks to an overall risk rather than being associated with variance-covariance based risk analysis. Considering the Solvency II Standard Formula from the viewpoint of linear geometry, we immediately find that it defines a norm and therefore provides a homogeneous and sub-additive tool for risk aggregation. Hence Euler's Principle for the reallocation of risk capital applies and yields explicit formulas for capital allocation in the framework given by the Solvency II Standard Formula. This gives rise to the definition of  diversification functions, which we define as monotone, subadditive, and homogeneous functions on a convex cone. Diversification functions constitute a class of models for the study of the aggregation of risk, and diversification. The aggregation of risk measures using a diversification function preserves the respective properties of these risk measures. Examples of diversification functions are given by seminorms, which are monotone on the convex cone of non-negative vectors. Each Lp norm has this property, and any scalar product given by a non-negative positive semidefinite matrix does as well. In particular, the Standard Formula is a diversification function and hence a risk measure that preserves homogeneity, subadditivity, and convexity.


Author(s):  
Wing Fung Chong ◽  
Runhuan Feng ◽  
Longhao Jin

AbstractRisk aggregation and capital allocation are of paramount importance in business, as they play critical roles in pricing, risk management, project financing, performance management, regulatory supervision, etc. The state-of-the-art practice often includes two steps: (i) determine standalone capital requirements for individual business lines and aggregate them at a corporate level; and (ii) allocate the total capital back to individual lines of business or at more granular levels. There are three pitfalls with such a practice, namely, lack of consistency, negligence of cost of capital, and disentanglement of allocated capitals from standalone capitals. In this paper, we introduce a holistic approach that aims to strike a balance of optimality by taking into account competing interests of various stakeholders and conflicting priorities in a corporate hierarchy. While unconventional in its objective, the new approach results in an allocation of diversification benefit, which conforms to the diversification strategy of many risk management frameworks including regulatory capital and economic capital. The holistic capital setting and allocation principle provides a remedy to aforementioned problems with the existing two-step industry practice.


2017 ◽  
Vol 72 ◽  
pp. 95-106 ◽  
Author(s):  
Tim J. Boonen ◽  
Andreas Tsanakas ◽  
Mario V. Wüthrich

2020 ◽  
Author(s):  
Wing Fung Chong ◽  
Runhuan Feng ◽  
Longhao Jin

1970 ◽  
Vol 10 (4) ◽  
pp. 491-499
Author(s):  
F. E. Banks

This note is an extension of several contributions to the problem of re¬source allocation in a developing economy. In separate papers, I.M.D. Little and F. Seton* have introduced a model in which labour in a developing economy cannot be shifted from the subsistence to the industrial sector at zero opportunity cost, even though this labour displays zero marginal product in its 'traditional' occupations; and in what follows this problem will be attacked via a diagramma¬tic analysis. A short appendix will treat a side issue of the topic. As Little presented the model, there was an initial amount of capital K to be divided between two sectors, the I (industrial) sector, and the C (subsistence, traditional, or agricultural) sector. In the C-sector, there is excess labour or dis¬guised unemployment, in the sense of Professor W. A. Lewis2, in that the marginal product of labour in this sector is taken as equal to zero. As it happens, however, this labour cannot be moved to the I-Sector without an increase in production in the C-sector. The reason for this is because as labour is transferred to the industrial sector, consumption per head increases in the C-sector, thus decreasing the surplus available for workers being transferred to the I-sector. The transfer can only be carried out if a surplus equal to the difference between the industrial wage in C-goods and the amount of C-goods 'released' by the C-sector is forth¬coming, and for this an increased production of C-goods (via the input of capital into the C-sector) must take place. A similar situation would exist if transferring workers required a wage differential; or if C-goods had to be exported to obtain certain types of capital goods for the labour being reallocated, and/or housing, training, etc.


Author(s):  
Iryna Nazarova

The paper considers various interpretations of the essence of equity capital. The concept of equity capital is viewed from the perspective of property as a venture capital, i. e. business property, which does not guarantee profits and dividends, and for which there is no clear schedule of returning funds to investors and shareholders. The most common equity capital components in national and foreign practice are examined and compared. It is pointed out that the equity components mainly used in Ukraine are defined by the National Accounting Standards. Alternatively, the structure of equity capital components in foreign practice relies on the Conceptual Framework of Financial Statements, but it is further detailed by national standards of each country and depends on its policy and accounting characteristics. The structure of equity capital in foreign practice may be influenced by shareholders’ decisions on the establishment of funds (additional capital), allocation of profits, transactions with treasury shares. It is made clear that in most countries equity capital components include joint stock capital, surplus reserves, and retained profit. The article reviews the classification of equity capital, viewed as the key factor, and determines its influence on accounting principles and policies. It is concluded that in regulatory documents, there are no clear lines between types of equity capital. The paper also discusses various views of scholars on equity capital arrangement. It is found that in research works, equity capital is classified based on various characteristics, but the majority of researchers consider sources of equity capital to be the main criterion. In addition, there is no consensus among academics as to what types of equity capital can be singled out by the criterion described. Taking into consideration some proposals of scholars and foreign practice related to ac- counting of equity capital, the author develops a generalized structure of equity capital which is based on the sources of capital formation and includes: invested capital, particularly registered capital (statutory and mandatory share capital), corrective capital (unpaid and withdrawn capital), additional capital (capital received from investors for stock that exceeds the par value of the stock, i.e. additional equity capital); acquired capital (assets received for free, capital formed from revaluation of assets, other capital) and reinvested capital (retained profits (uncovered losses) and surplus reserves). The above equity structure can be used to prepare financial statements in order to increase its informational value. Proposals are given on how to improve methods for accounting of equity capital, in particular accounting of additional capital invested by founders in the account entitled “Non-registered investments of owners”.


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