The explicit form of no arbitrage condition when the term structure model is multi-factor

The no arbitrage conditions are derived in the explicit form for the market, where the zero coupons bonds of various maturities are accessible for the investors to draw up the portfolios. It is supposed, that the investor at any moment of time has a possibility to make the self-financed portfolio of given value. It is considered that the processes of the short interest rate and rates of inflation follow the stochastic differential equations. The known result for a portfolio with two assets is extended on case of any number of assets and inflation. The no arbitrage condition for multi-factor models of a term structure of the interest rates is considered. The condition of existence of a risk free self-financed portfolio is obtained at first, and then for want of it fulfillment the no arbitrage condition is derived