The main goal of this chapter is to show how the general theory developed before can be applied to mathematical finance and statistics of random processes. In the area of mathematical finance, a semimartingale financial market model is introduced. Applying to this general model the technique of stochastic exponents, the fundamental questions of arbitrage and completeness of such a market are studied. These results have a number of corollaries for modeling and option pricing (Black-Scholes model and formula, Cox-Ross-Rubinstein model and formula, etc.). In the area of statistics of random processes, the technique developed above gives a possibility to introduce semimartingale models. It is shown that classical discrete time and continuous time models of stochastic approximation are embedded in a semimartingale scheme. Moreover, it is proved that semimartingale stochastic approximation procedures are strong consistent and asymptotically normal under very wide conditions. In case of semimartingale regression, the structural least-squares estimates are strong consistent and their sequential versions satisfy the important Fixed accuracy property fixed accuracy property (see Bishwal, Parameter estimation in stochastic differential equations, 2008; Borkar, Stochastic approximation: a dynamical systems viewpoint, 2008; Eberlein and Kallsen, Mathematical finance, 2019; Etheridge, A course in financial calculus, 2002; Klebaner, Introduction to stochastic calculus with applications, 2012; Lamberton and Lapeyre, Introduction to stochastic calculus applied to finance, 1996; Melnikov, Russian Math Surv 51(5):43–136, 1996; Nevel’son and Has’minskii, Stochastic approximation and recursive estimation, 1976, and Valkeila and Melnikov, Theory Probab Appl 44(2):333–360, 2000).