Unified And Hybrid Approaches To Identification, Optimization And Control Of Stochastic Financial Processess-Theory, Methods And Applications.

Date

2012-12-31

Author

Weber, Gerhard Wilhelm

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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 theory and algorithms. Alternatively, when following the Martingale Method of Portfolio Optimization, one can also arrive at a stepwise treatment of (i) and (ii), in fact, at a Tri-Level Problem, for which methods of optimization theory and stochastic calculus can be developed. If the parameter estimation is done in a last step, then the martingale method with its two steps is understood in a parametric sense of optimization. Let us remark that a significant contribution to this project was given by the recently finalized BAP project of 2010 “Identification, Optimization and Control of Stochastic Differential Equations in Financial Mathematics”. The use of our GAM & CQP on SDEs was already worked out, now we shall demonstrate the use of our CMARS for SDEs. All of this can also be done for systems of SDEs of various kinds, and with facing the presence of jump processes (i.e., for Lévy processes, incomplete markets), too. Moreover, we are considering the use of other methods, such as Bayesian and Maximum Likelihood Estimation, and of given algorithms / program packages, and the comparison of our techniques with them. When treating parameter estimation and portfolio optimization in a stepwise manner, we discuss and apply different methods from Multi-Level Optimization and Analysis. Finally, as an alternative of varities of the Martingale Method, we also use Stochastic Control, especially, Stochastic Hybrid Control.

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https://hdl.handle.net/11511/61677

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Graduate School of Applied Mathematics, Project and Design

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Citation Formats

G. W. Weber, “Unified And Hybrid Approaches To Identification, Optimization And Control Of Stochastic Financial Processess-Theory, Methods And Applications.,” 2012. Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/61677.