Stochastic Modeling and Financial Applications

Simulation of Stochastic Processes in Financial Modeling

This paper discusses theoretical properties, shows the performance and presents some extensions of techniques used for simulation of stochastic differential equation applied on the financial data modeling. There are realized comparisons of different approaches for discretization schemes and their performances from the simulation convergence point of view. This study shows that, depending on the...

Stochastic orders and their applications in financial optimization

Stochastic orders and inequalities are very useful tools in various areas of economics and finance. The purpose of this paper is to describe main results obtained so far by using the idea of stochastic orders in financial optimization. Especially, the emphasis is placed on the demand and shift effect problems in portfolio selection. Some other examples, which are not related directly to optimiz...

Stochastic Delay Difference and Differential Equations: Applications to Financial Markets

This thesis deals with the asymptotic behaviour of stochastic difference and functional differential equations of Itô type. Numerical methods which both minimise error and preserve asymptotic features of the underlying continuous equation are studied. The equations have a form which makes them suitable to model financial markets in which agents use past prices. The second chapter deals with the...

Stochastic Processes and their Applications in Financial Pricing

Anticipative Stochastic Calculus with Applications to Financial Markets

In this thesis, we study both local time and Malliavin calculus and their application to stochastic calculus and finance. In the first part, we analyze three aspects of applications of local time. We first focus on the existence of the generalized covariation process and give an approximation when it exists. Thereafter, we study the decomposition of ranked semimartingales. Lastly, we investigat...