### Journals Information

**
Universal Journal of Physics and Application Vol. 8(1), pp. 48 - 52 DOI: 10.13189/ujpa.2014.020109 Reprint (PDF) (88Kb) **

## Prognostic Example of Stochastic Approach

**Wolodymyr Hlib KOZYRSKI ^{*}**

The Bogolubov Institute for Theoretical Physics,Ukrainian National Academy of Sciences,Kiev, 03680, Ukraine

**ABSTRACT**

The paper contains an application of Gonchar banking model to estimate default probability under random claim attack. We model investment environment by a sequence of random values characterizing risks under investing. Constructed model takes into account receipt of deposits to the accounts of bank and obligations fulfilment to return deposits with interest and other liabilities too. We model repayments by sequence of independent equally distributed random values depending on liabilities that can be fixed in various way. Constructed model is Markov homogeneous chain with transition function for one step that determined by probabilities of investment risk and distribution function of repayments. We consider a case when the distribution of payments has a ”non-zero tails.” We proved constructive theorems evaluating the probability of bankruptcy. The estimate depends on the probability of the capital loss due to systematic risk, the value of bad loans, initial capital, a minimum level of profitability, and determines the initial capital value for which the bank can operate without bankrupting for a long time under a relatively low probability of systematic risk. We have obtained the explicit expression for such initial capital. Therefore, Gonchar banking model lays a solid ground to estimate bank default risk in practice.

**KEYWORDS**

Banking, Bankruptcy, Financial Sta- bility, N. S.Gonchar Banking Model, Random Claim Attack

**Cite this paper**

Wolodymyr Hlib KOZYRSKI . "Prognostic Example of Stochastic Approach." Universal Journal of Physics and Application 8.1 (2014) 48 - 52. doi: 10.13189/ujpa.2014.020109.