Identification, Optimization and Control of Stochastic Differential Equations in Financial Mathematics

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2010-12-31

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Weber, Gerhard Wilhelm

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Identification, Optimization and Control of Stochastic Differential Equations in Financial Mathematics

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https://hdl.handle.net/11511/61665

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Graduate School of Applied Mathematics, Project and Design

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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...
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...
Identification of coupled systems of stochastic differential equations in finance including investor sentiment by multivariate adaptive regression splines Kalaycı, Betül; Weber, Gerhard Wilhelm; Department of Financial Mathematics (2017) Stochastic Differential Equations (SDEs) rapidly become the most well-known format in which to express such diverse mathematical models under uncertainty such as financial models, neural systems, micro-economic systems, and human behaviour. They are one of 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 several empirical phenomena...
Dynamics of numerical methods for cosymmetric ordinary differential equations Govorukhin, VN; Tsybulin, VG; Karasözen, Bülent (2001-09-01) The dynamics of numerical approximation of cosymmetric ordinary differential equations with a continuous family of equilibria is investigated. Nonconservative and Hamiltonian model systems in two dimensions are considered and these systems are integrated with several first-order Runge-Kutta methods. The preservation of symmetry and cosymmetry, the stability of equilibrium points, spurious solutions and transition to chaos are investigated by presenting analytical and numerical results. The overall performan...

Citation Formats

G. W. Weber, “Identification, Optimization and Control of Stochastic Differential Equations in Financial Mathematics,” 2010. Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/61665.