2013/02/12 by Shiqi Song, Song, Shiqi · 3 citations
Mathematics · Economics, Econometrics and Finance · #Differential Equations and Numerical Methods #Stochastic processes and financial applications #Differential Equations and Boundary Problems
paper · pdf · doi:10.48550/arxiv.1302.2862
The enlargement of filtration theory is a study of semimartingales when the basic filtration changes. This theory provides particular techniques on stochastic calculus. We present here a technique, that we call the local solution method. We will show, with several examples, that the local solution method is an effective and flexible method. In particular, with the local solution method, we will give a unified proof of three of the classical formulas, namely Jacod's formula, the progressive enlargement formula and the enlargement formula with honest time. We also show that, besides its generality, this method, necessiting long (but interesting) computations, may not be optimal.