Stochastic Hybrid Systems of Financial and Economical Processess: Identificatied, Optimized and Controlled

Weber, Gerhard Wilhelm
Yolcu Okur, Yeliz
Yerlikaya Özkurt, Fatma
Kuter, Semih
Özmen, Ayşe
Karimov, Azar
This research project will scientifically broaden, deepen and apply a scientific unified approach of both identification and optimal control of Stochastic Differential Equations with Jumps (SHSJs), motivated by and foreseen for purposes of financial mathematics and actuarial sciences. SHSJs and further structured and detailed models are in the scope of our framework, and special interests pursued consisted in a. refinement of Parameter Estimation for SDEs and b. Portfolio Optimization and, as a future extension,c. selected aspects of option pricing, e.g., (hitting- or stopping-) Time Maximal Stochastic Control.Our project used and further enriched and refined methods from Stochastic Calculus, Continuous (Conic) Optimization and of Inverse Problems Theory for compromised goals of accurate / optimized and regularized / risk-controlled modeling of financial process, and their programming and optimal control. This serves to provide solutions to challenges from the financial practice of the micro and macro economical level, and to enrich and develop the fine analytical techniques of finanical mathematics, for the people of Turkey and the world. In fact, optimal control is one of the popular techniques used for solving discrete-continuous time (hybrid) portfolio optimization problems. Our optimal control techniques include a powerful recursive algorithm that selects the optimal policy for the current state on an optimized path of future policies.


Unified And Hybrid Approaches To Identification, Optimization And Control Of Stochastic Financial Processess-Theory, Methods And Applications.
Weber, Gerhard Wilhelm(2012-12-31)
This research project aims at a new unified view onto both identification and optimal control of Stochastic Differential Equations (SDEs) for purposes of financial mathematics and actuarial sciences. More specific cases such as Stochastic Hybrid Systems are also considered in this framework. A special interests consists in (i) refinement of Parameter Estimation for SDEs and (ii) Portfolio Optimization. Here, the words “unified” or “joint” mean an integrated and simultaneous treatment of (i) and (ii) in the...
Mutual relevance of investor sentiment and finance by modeling coupled stochastic systems with MARS
Kalayci, Betul; Ozmen, Ayse; Weber, Gerhard Wilhelm (Springer Science and Business Media LLC, 2020-08-01)
Stochastic differential equations (SDEs) rapidly become one of the most well-known formats in which to express such diverse mathematical models under uncertainty such as financial models, neural systems, behavioral and neural responses, human reactions and behaviors. They belong to the main methods to describe randomness of a dynamical model today. In a financial system, different kinds of SDEs have been elaborated to model various financial assets. On the other hand, economists have conducted research on s...
Asymptotic integration of impulsive differential equations
Doğru Akgöl, Sibel; Ağacık, Zafer; Özbekler, Abdullah; Department of Mathematics (2017)
The main objective of this thesis is to investigate asymptotic properties of the solutions of differential equations under impulse effect, and in this way to fulfill the gap in the literature about asymptotic integration of impulsive differential equations. In this process our main instruments are fixed point theorems; lemmas on compactness; principal and nonprincipal solutions of impulsive differential equations and Cauchy function for impulsive differential equations. The thesis consists of five chapters....
Numerical studies of Korteweg-de Vries equation with random input data
Üreten, Mehmet Alp; Yücel, Hamdullah; Uğur, Ömür; Department of Scientific Computing (2018)
Differential equations are the primary tool to mathematically model physical phenomena in industry and natural science and to gain knowledge about its features. Deterministic differential equations does not sufficiently model physically observed phenomena since there exist naturally inevitable uncertainties in nature. Employing random variables or processes as inputs or coefficients of the differential equations yields a stochastic differential equation which can clarify unnoticed features of physical event...
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
G. W. Weber, Y. Yolcu Okur, F. Yerlikaya Özkurt, S. Kuter, A. Özmen, and A. Karimov, “Stochastic Hybrid Systems of Financial and Economical Processess: Identificatied, Optimized and Controlled,” 2013. Accessed: 00, 2020. [Online]. Available: