The model оf outside debt and money dynamics is given by two stochastic differential equations. Solutions of the system represent different regimes of outside debt monetization. Government liabilities form the nominal anchor while rational, risk-aver­se investors take different positions with respect to outside debt and money in a process of continuous delta hedging. The level of outside money issuance that guarantees the normal monetization maximizes the market value of new debts while hedging out risks of the default on debt. The probability of hyperinflation and the debt collapse becomes strictly nonzero should this threshold be exceeded. The model identification was performed on Russian data including the debt crisis in August 1998.