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New Approaches To Risk Management And Scenario Approximation In Financial Optimization, Maksym Bychkov

Doctoral Dissertations

The first part of the thesis addresses the problem of risk management in financial optimization modeling. Motivation for constructing a new concept of risk measurement is given through the history of development: utility theory, risk/return tradeoff, and coherent risk measures. The process of describing investor's preferences is presented through the proposed collection of Rational Level Sets (RLS). Based on RLS, a new concept termed Rational Risk Measures (RRM) for nancial optimization models is defined. The advantages of RRM over coherent risk measures are discussed. Approximation of a given set of scenarios using tail information is addressed in the second part …