On Pathwise Stochastic Integration of Processes with Unbounded Power Variation

Zhe Chen

Tutkimustuotos: Doctoral ThesisMonograph

Abstrakti

This dissertation concerns pathwise integrability of stochastic processes which are non-semimartingales with unbounded power variation. In this dissertation, a class of stochastic processes which can be represented as a composition of a Hölder continuous process with a nonrandom function of locally bounded variation is studied. Since the nonrandom function may contain discontinuities, stochastic processes in this class are usually of unbounded power variation. This kind of stochastic processes are of interest in many applications, for example in financial mathematics concerning option pricing. In this dissertation, new conditions are presented for the existence of generalized Lebesgue–Stieltjes integrals for the aforementioned one-dimensional stochastic processes with respect to general Hölder continuous processes. This dissertation also contains a new result on the existence of generalized Lebesgue–Stieltjes integrals for a certain class of multi-dimensional stochastic processes with respect to general Hölder continuous processes. Moreover, in this dissertation, a new proof is presented for a change of variables formula for sufficiently regular one-dimensional stochastic processes with unbounded power variation.
Julkaisun otsikon käännösOn Pathwise Stochastic Integration of Processes with Unbounded Power Variation
AlkuperäiskieliEnglanti
PätevyysTohtorintutkinto
Myöntävä instituutio
  • Aalto-yliopisto
Valvoja/neuvonantaja
  • Leskelä, Lasse, Vastuuprofessori
  • Viitasaari, Lauri, Ohjaaja
Kustantaja
Painoksen ISBN978-952-60-6671-4
Sähköinen ISBN978-952-60-6672-1
TilaJulkaistu - 2016
OKM-julkaisutyyppiG4 Tohtorinväitöskirja (monografia)

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