Decision support modeling via multivariate risk measures and stochastic optimization

Abstract

OF THE DISSERTATION Decision Support Modeling via Multivariate Risk Measures and Stochastic Optimization by Jinwook Lee Dissertation Director: Andras Prekopa Whenever we have a decision to make, there is always some risk to take. From a mathematical perspective, risk is manifested by a random variable, and a risk measure simply characterizes the random variable in a more compact form. Risk, in general and in practice, is not be adequately described by a real valued random variable, but rather requires a random vector to capture the dimensions of the problem. To this end, multivariate risk measures are crucial ingredients for decision making processes, and stochastic optimization is a natural and superior skill to find a key to the optimal decision-making. A recent paper by Prekopa (2012) presented results in connection with Multivariate Value-at-Risk (MVaR) that has been known for some time under the name of p-quantile or p-Level Efficient Point (pLEP) and introduced a new multivariate risk measure, called Multivariate Conditional Value-at-Risk (MCVaR). Lee and Prekopa (2013) studied new methods for numerical calculations and mathematical properties of these multivariate risk measures, presented in Chapter 2. Another new multivariate risk measure has been constructed and presented in Chapter 3. This is especially for