To make good decisions to not to face uncertainty, mathematical finance helps quite a lot. Building on the mathematical models of bonds and the stocks prices, simulation theories for mathematical financing vary with leads in different directions: Black-Scholes arbitrage pricing of options is one of the significant revealing theories used extensively in mathematical financing research and studies. Markowitz portfolio optimization for a capital asset pricing modeling is another crucial research target.
Interest rates and the terms structure can be best understood with the principle of no arbitrage. Mathematical finance is best studied with all these three essentials explained. The modern financial markets are operating this way. There is enormous impact of mathematical finance modeling in business management and business economics.