On linear stochastic equations of optional semimartingales and their applications. (English) Zbl 1377.60067
Summary: Elements of the stochastic calculus of optional semimartingales are presented. A solution of the nonhomogeneous and general linear stochastic equations is given in this framework. Also, the Gronwall inequality is derived. Furthermore, a theory of martingale transforms and examples of applications to mathematical finance are presented.
MSC:
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60G48 | Generalizations of martingales |
References:
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