Abstract
Chapter 1 provides a relevant field of application for the computation of functionals of multidimensional diffusions. The chapter introduces a unified continuous time framework for financial and insurance modeling. This framework can be applied to portfolio optimization, derivative pricing, financial modeling, actuarial pricing and risk measurement. The basis for this framework is the “benchmark approach” developed by Platen and collaborators. Under the benchmark approach, the best performing, strictly positive portfolio is chosen as natural numéraire for pricing. This portfolio is the growth optimal portfolio, which maximizes expected growth or log-utility. Also, it is the numéraire portfolio such that any nonnegative portfolio denominated in units of this portfolio turns out to be a supermartingale. This important property leads to a natural pricing rule under the real world probability measure, which identifies the minimal replicating price. An important property of the benchmark approach is that unlike the classical risk neutral paradigm, it does not rely on the existence of a risk neutral probability measure. This provides the modeler with significantly more freedom, as it means that not only models covered by the classical risk neutral paradigm can be studied, but a much wider range. The focus of this book will be on tractable models, which may go beyond the classical risk neutral paradigm, and the computation of important functions in these models.
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Baldeaux, J., Platen, E. (2013). A Benchmark Approach to Risk Management. In: Functionals of Multidimensional Diffusions with Applications to Finance. Bocconi & Springer Series, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-319-00747-2_1
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DOI: https://doi.org/10.1007/978-3-319-00747-2_1
Publisher Name: Springer, Cham
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