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Continuous-time stochastic modelling of capital adequacy ratios for banks. (English) Zbl 1126.60053

This paper deals with the construction of stochastic models for the dynamics of risk-based capital adequacy ratio and non-risk-based capital adequacy ratio in continuous-time. For each of the aforementioned types of capital adequacy ratio a stochastic differential equation is produced that highlight some of the dynamic features of the bank’s on- and off-balance sheet activities. Each of the banking items (asset, liabilities, bank capital, off-balance sheet items) is modelled separately with the dynamics of the capital adequacy ratio ultimately being expressed in terms of these components. The authors make use of stochastic calculus to formalize the most important properties of the listed above banking items. Credit, market and operational risk is considered from the idiosyncratic viewpoint of the internal rating based, internal model and standardized approaches, respectively. It is demonstrated how the obtained main results may be applied in the banking sector.

MSC:

60H30 Applications of stochastic analysis (to PDEs, etc.)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
62-07 Data analysis (statistics) (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
91B28 Finance etc. (MSC2000)
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