@MISC{FINANCE5.MIZ,
  AUTHOR = {Jaeger, Peter},
  TITLE = {Introduction to Stopping Time in Stochastic Finance Theory: Part {II}},
  SECTION1 = {Theory of Stopping Time in Discrete Time},
  SECTION2 = {Theory of Stopping Time in Continuous Time},
  SECTION3 = {Borel-Sets}
  SECTION3 = {$\sigma$-Algebra of the $\tau$-past}
  DAY = {29},
  MONTH = {November},
  YEAR = {2017},
  ADDRESS1 = {},
  SUMMARY = {We start proceeding with stopping time theory in discrete time.
             We show, the necessity in
             (\cite{follmerschied:2004},p.283), that in general the expression
             for two stopping times tau1,tau2 not always implies
             a stoppingtime (tau1+tau2). This means you have to cut it
             - (tau+sigma)/\T (in the case of finity) -.
             Next we introduce stopping time in continuouos time.
             Here we are focused on the time intervales [.0.r.] where r in REAL
             and [.0,+infty.[ We prove some Borel-Sets,more general given in
             (\cite{georgii:2004}, p.~12 1.8,(e)). These Borel-Sets are neccessary
             to define our nex theorem. In the case of continuity we show, that
             the \sigma-algebra of the \tau-past, where \tau is a
             stopping time has a certain characteristic
             (\cite{klenke:2006}, p.~187, Definition 9,19 and Lemma 9.21).
             Stopping Times can be used together with the conditional
             expected value. Look as an example to the Optional Sampling
             Theorem in \cite{klenke:2006}, p.~203.}}

@book{follmerschied:2004,
  author={F\"ollmer, Hans and Schied, Alexander},
  title={Stochastic Finance: An Introduction in Discrete Time},
  edition={2nd},
  volume={27},
  series={Studies in Mathematics},
  publisher={de Gruyter},
  year={2004},
  ADDRESS={Berlin}}

@book{klenke:2006,
author={Klenke, Achim},
title={Wahrscheinlichkeitstheorie},
publisher={Springer-Verlag},
year={2006},
ADDRESS={Berlin, Heidelberg}}

@book{georgii:2004,
author={Georgii, Hans-Otto},
title={Stochastik, Einf\"uhrung
  in die Wahrscheinlichkeitstheorie und Statistik},
edition={2},
publisher={deGruyter},
year={2004},
ADDRESS={Berlin}}
