New approaches to Risk Management and Scenario Approximation in Financial Optimization
作者： Maksym Bychkov
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摘要: The first part of the thesis addresses problem risk management in financial optimization modeling. Motivation for constructing a new concept measurement is given through history development: utility theory, risk/return tradeoff, and coherent measures. process describing investor’s preferences presented proposed collection Rational Level Sets (RLS). Based on RLS, termed Risk Measures (RRM) models defined. advantages RRM over measures are discussed. Approximation set scenarios using tail information addressed second thesis. scenario approximation problem, as way reducing computation time preserving solution accuracy, examples asset allocation models. Using basic ideas Conditional Value at (CVaR), this develops methodology stochastic portfolio optimization. First, concepts Scenarios-at-Risk (SaR) Scenarios-at-Gain (SaG) purpose partitioning underlying multivariate domain fixed investment probability level CVaR. Then, under CVaR values, twostage method developed determining smaller, discrete, which control satisfied all portfolios interest. Convergence shown numerical results to validate technique.
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