Advanced Mathematical Methods of Financial Risk Management Investigated and Solved by New Methods of Stochastic Calculus, Mathematical Statistics and Optimization

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2010-12-31

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Weber, Gerhard Wilhelm

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Advanced Mathematical Methods of Financial Risk Management Investigated and Solved by New Methods of Stochastic Calculus, Mathematical Statistics and Optimization

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https://hdl.handle.net/11511/61664

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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...
Advenced Mathematical Methods of Quality Analysis and Improvement by Nevw Methods of Computational Statistics and with Applications in Manufacturing and Finance Weber, Gerhard Wilhelm(2010-12-31) Advenced Mathematical Methods of Quality Analysis and Improvement by Nevw Methods of Computational Statistics and with Applications in Manufacturing and Finance
Identification, Optimization and Control of Stochastic Differential Equations in Financial Mathematics Weber, Gerhard Wilhelm(2010-12-31) Identification, Optimization and Control of Stochastic Differential Equations in Financial Mathematics
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...
Advances in optimal control of markov regime-switching models with applications in finance and economics Savku, Emel; Weber, Gerhard Wilhelm; Department of Financial Mathematics (2017) We study stochastic optimal control problems of finance and economics in a Markov regime-switching jump-diffusion market with and without delay component in the dynamics of our model. We formulate portfolio optimization problems as a two player zero-sum and a two player nonzero-sum stochastic differential games. We provide an extension of Dynkin formula to present the Hamilton-Jacobi-Bellman-Isaacs equations in such a more general setting. We illustrate our results for a nonzero-sum stochastic differential ...

Citation Formats

G. W. Weber, “Advanced Mathematical Methods of Financial Risk Management Investigated and Solved by New Methods of Stochastic Calculus, Mathematical Statistics and Optimization,” 2010. Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/61664.