Use this URL to cite or link to this record in EThOS: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.794074
Title: Stochastic calculations with applications to finance
Author: Wang, Kuo
ISNI:       0000 0004 8498 3648
Awarding Body: University of Leicester
Current Institution: University of Leicester
Date of Award: 2019
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Abstract:
This thesis presents a variety of probabilistic and stochastic calculations related to the Ornstein-Uhlenbeck process, the weighted self-normalized sum of exchangeable variables, various operators defined on the Wiener space and Greeks in mathematical finance. First, we discuss some properties of the weighted self-normalized sum of exchangeable variables. Then we show two methods to compute the different order moments of the Brownian motion via the definition of expactation and the so-called Malliavin calculus, repectively. We also show how to compute the different order moments of the Ornstein- Uhlenbeck process by using Itô calculus and generlize it to the Itô processes of the Ornstein- Uhlenbeck type. Finally we show how to apply the Malliavin calculus to compute different operators defined on the Wiener space such as the derivative opertor, the divergence opertor, the infinitesimal generator of the Ornstein-Uhlenbeck semigroup and the associated characteristics. We also apply Malliavin calculus to compute Greeks for European options as well as exotic options, where the integration by parts formula provides a powerful tool. In addition, we demonstrate the computation of Greeks for the models where we treat share price Itô martingale models such as Wt and Wt2−t.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.794074  DOI:
Keywords: Stochastic Calculations ; Thesis
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