No arbitrage condition for financial market with inflation

Abstract

When price dynamics in the financial market is modeled as a continuous-time mathematical model, it is assumed that the interest rates in the market follow stochastic differential equations. The noarbitrage condition in that market with inflation is obtained for a portfolio with any number of assets. Also it is derived from explicit form the no-arbitrage condition in the segmented market (without inflation), where it is considered that in the market there simultaneously are some segments, in which bonds with hardly distinguishable maturation enter and each segment has its own risk-free interest rate. It is considered that in this situation the investor has a possibility to purchase the bonds of any segment.