Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
Backward stochastic differential equations and their applications to stochastic control problems
Download
index.pdf
Date
2013
Author
Nalbant, Hanife Sevda
Metadata
Show full item record
Item Usage Stats
33
views
16
downloads
Cite This
Backward stochastic di fferential equations (BSDE) were firstly introduced by Bismut in 1973. Following decades, it has been great interest all over the world and appeared in numerious areas such as pricing and hedging claims, utility theory and optimal control theory. In 1997, El Karoui, Peng and Quenez brought together their brilliant studies in the article Backward Stochastic Di fferential Equations in Finance. They considered an adapted solution pair (Y,Z) of the following BSDE: -dY_t = f(t, Y_t,Z_t)dt - Z _t^* dW_t with the terminal value Y_T =\xi . Here Z^* corresponds to the transpose of the n xn matrix Z, f is called the generator and \xi is the terminal condition. In this thesis, we study some chapter of this paper in detail. We prove the fundamental theorems of backward stochastic diff erential equations and associate them with stochastic control problems. After we prove the existence of unique solution using a Priori estimates under some restrictions, we show how to choose the optimal stochastic control that achieves the best utility or the least cost. At the end of the thesis, we o ffer an optimal choice for the solution of the BSDE in the cases of the standard generator f is concave or convex. An application for the model with consumption and an application for hedging claims with higher interest rate for borrowing are provided.
Subject Keywords
Stochastic differential equations.
,
Stochastic control theory.
,
Hedging (Finance).
,
Pricing.
URI
http://etd.lib.metu.edu.tr/upload/12615950/index.pdf
https://hdl.handle.net/11511/22652
Collections
Graduate School of Applied Mathematics, Thesis
Suggestions
OpenMETU
Core
Backward stochastic differential equations and Feynman-Kac formula in the presence of jump processes
İncegül Yücetürk, Cansu; Yolcu Okur, Yeliz; Hayfavi, Azize; Department of Financial Mathematics (2013)
Backward Stochastic Differential Equations (BSDEs) appear as a new class of stochastic differential equations, with a given value at the terminal time T. The application area of the BSDEs is conceptually wide which is known only for forty years. In financial mathematics, El Karoui, Peng and Quenez have a fundamental and significant article called “Backward Stochastic Differential Equations in Finance” (1997) which is taken as a groundwork for this thesis. In this thesis we follow the following steps: Firstl...
Advances and applications of stochastic Ito-Taylor approximation and change of time method in the financial sector
Öz, Hacer; Weber, Gerhard Wilhelm; Department of Financial Mathematics (2013)
In this thesis, we discuss two different approaches for the solution of stochastic differential equations (SDEs): Ito-Taylor method (IT-M) and change of time method (CT-M). First approach is an approximation in space-domain and the second one is a probabilistic transformation in time-domain. Both approaches may be considered to substitute SDEs for more “practical” representations and solutions. IT-M was most studied for one-dimensional SDEs. The main aim of this work is to extend the theory of one-dimension...
Quantitative measures of observability for stochastic systems
Subaşı, Yüksel; Demirekler, Mübeccel; Department of Electrical and Electronics Engineering (2012)
The observability measure based on the mutual information between the last state and the measurement sequence originally proposed by Mohler and Hwang (1988) is analyzed in detail and improved further for linear time invariant discrete-time Gaussian stochastic systems by extending the definition to the observability measure of a state sequence. By using the new observability measure it is shown that the unobservable states of the deterministic system have no effect on this measure and any observable part wit...
Least squares differential quadrature time integration scheme in the dual reciprocity boundary element method solution of convection-diffusion problems
Bozkaya, Canan (2005-03-18)
The least squares differential quadrature method (DQM) is used for solving the ordinary differential equations in time, obtained from the application of the dual reciprocity boundary element method (DRBEM) for the spatial partial derivatives in convection-diffusion type problems. The DRBEM enables us to use the fundamental solution of the Laplace equation which is easy to implement computationally. The time derivative and the convection terms are considered as the nonhomogeneity in the equation which are ap...
Two studies on backward stochastic differential equations
Tunç, Vildan; Sezer, Ali Devin; Department of Financial Mathematics (2012)
Backward stochastic differential equations appear in many areas of research including mathematical finance, nonlinear partial differential equations, financial economics and stochastic control. The first existence and uniqueness result for nonlinear backward stochastic differential equations was given by Pardoux and Peng (Adapted solution of a backward stochastic differential equation. System and Control Letters, 1990). They looked for an adapted pair of processes {x(t); y(t)}; t is in [0; 1]} with values i...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
H. S. Nalbant, “Backward stochastic differential equations and their applications to stochastic control problems,” M.S. - Master of Science, Middle East Technical University, 2013.