Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.mce.biophys.msu.ru/archive/doc144724/eng.pdf Дата изменения: Sun Mar 23 02:14:34 2014 Дата индексирования: Sun Mar 23 02:14:34 2014 Кодировка:

Bi-stable model of risk interest rate. Krivosheev Oleg Igorevich, chair of Applied Mathematics MESI, 8-926-593-75-46, okrivosheev@mail. ru Variables ­ an amount of dept per unit of productive capital, 1- ­ own capital, r ^ variable is slow, r - risk, r - normalized risk. b - risky bank interest rate b b0 r , d where b0 - risk less interest rate: for the sake of simplicit y b0 0 , and thus b r . Parameters. - time of refinance o f debt, iF - internal rate of return of capital, iob internal rate of return o f current capital, d ­ depreciation rate, ­ ratio of current capital to the total capital, 1 - ratio of lo ng term capital to the total capital, i / d dimensio nless rate of return. If r - is an intensit y of rn+1 . 1. the Poisson flow of bankruptcy, than tb r 1 - is a n average t ime before the bankruptcy, at the level of risk rate r=b, time of bankruptcy may be est imated as a time of achieving o f boarder where 1 (or d simply 1 ) b (iF d ) d , let us dt suppose that the velocit y of dept changing or growth 1 is constant v b (iF d ) d , than, using r rn tb we obtain a discrete mapping o f interest into itself rn1 rn d . Since risk is not 1 0 negat ive one should be rewrited rn 1 max(0, rn d ) . Risk interest rate should be 1 0 1 bounded wit h rmax ( 1 1)d , - the rate of return of current assets: rn1 min(max( 0, rn d ), rmax ) . Equilibriums are the fo llowing r rmax - crisis, 1 0 10 rus d unstable & r 0 is the 2 1 0 Crisis is very preferable one. They meet rn1 rn . There is no probable . 2. 2 crisis equilibrium if 1 , at plane =1 Crisis not 1 dominates, =0 this means that 2 , - see curved line but possible in Fig 2. Lower equilibrium is the main one or have No crisis hire potential when we see 2 1 or possible 2 (this is so lut ion for condit ion 2rus rmax ). One may consider it as a boarder of =1/2 =1 financial stabilit y o f economy & single enterprise.