A Semi-Infinite Programming Approach for Distributionally Robust Reward-Risk Ratio Optimization with Matrix Moments Constraints

Reward-risk ratio optimization is an important mathematical approach in finance. In this paper, we revisit the model by considering a situation where an investor does not have complete information on the distribution of the underlying uncertainty and consequently a robust action is taken against the risk arising from ambiguity of the true distribution. We propose … Read more

Robust Growth-Optimal Portfolios

The growth-optimal portfolio is designed to have maximum expected log-return over the next rebalancing period. Thus, it can be computed with relative ease by solving a static optimization problem. The growth-optimal portfolio has sparked fascination among finance professionals and researchers because it can be shown to outperform any other portfolio with probability 1 in the … Read more

Ambiguous Probabilistic Programs

Probabilistic programs are widely used decision models. When implemented in practice, however, there often exists distributional ambiguity in these models. In this paper, we model the ambiguity using the likelihood ratio (LR) and use LR to construct various ambiguity sets. We consider ambiguous probabilistic programs which optimize under the worst case. Ambiguous probabilistic programs can … Read more

A practicable framework for distributionally robust linear optimization

We developed a modular framework to obtain exact and approximate solutions to a class of linear optimization problems with recourse with the goal to minimize the worst-case expected objective over an ambiguity set of distributions. The ambiguity set is specified by linear and conic quadratic representable expectation constraints and the support set is also linear … Read more

Distributionally robust control of constrained stochastic systems

We investigate the control of constrained stochastic linear systems when faced with only limited information regarding the disturbance process, i.e. when only the first two moments of the disturbance distribution are known. We consider two types of distributionally robust constraints. The constraints of the first type are required to hold with a given probability for … Read more