Relative Robust Portfolio Optimization

Considering mean-variance portfolio problems with uncertain model parameters, we contrast the classical absolute robust optimization approach with the relative robust approach based on a maximum regret function. Although the latter problems are NP-hard in general, we show that tractable inner and outer approximations exist in several cases that are of central interest in asset management

Robust Portfolio Optimization with Derivative Insurance Guarantees

Robust portfolio optimization aims to maximize the worst-case portfolio return given that the asset returns are allowed to vary within a prescribed uncertainty set. If the uncertainty set is not too large, the resulting portfolio performs well under normal market conditions. However, its performance may substantially degrade in the presence of market crashes, that is, if the asset returns materialize far outside of the uncertainty set. We propose a novel robust portfolio optimization model that provides additional strong performance guarantees for all possible realizations of the asset returns. This insurance is provided via optimally chosen derivatives on the assets in the portfolio. The resulting model constitutes a convex second- order cone program, which is amenable to efficient numerical solution. We evaluate the model using simulated and empirical backtests and conclude that it can out- perform standard robust portfolio optimization as well as classical mean-variance optimization.robust optimization, portfolio optimization, portfolio insurance, second order cone programming

Decision Sciences, Economics, Finance, Business, Computing, and Big Data: Connections

This paper provides a review of some connecting literature in Decision Sciences, Economics, Finance, Business, Computing, and Big Data. We then discuss some research that is related to the six cognate disciplines. Academics could develop theoretical models and subsequent econometric and statistical models to estimate the parameters in the associated models. Moreover, they could then conduct simulations to examine whether the estimators or statistics in the new theories on estimation and hypothesis have small size and high power. Thereafter, academics and practitioners could then apply their theories to analyze interesting problems and issues in the six disciplines and other cognate areas

Distributionally robust optimization with applications to risk management

Many decision problems can be formulated as mathematical optimization models. While deterministic optimization problems include only known parameters, real-life decision problems almost invariably involve parameters that are subject to uncertainty. Failure to take this uncertainty under consideration may yield decisions which can lead to unexpected or even catastrophic results if certain scenarios are realized. While stochastic programming is a sound approach to decision making under uncertainty, it assumes that the decision maker has complete knowledge about the probability distribution that governs the uncertain parameters. This assumption is usually unjustified as, for most realistic problems, the probability distribution must be estimated from historical data and is therefore itself uncertain. Failure to take this distributional modeling risk into account can result in unduly optimistic risk assessment and suboptimal decisions. Furthermore, for most distributions, stochastic programs involving chance constraints cannot be solved using polynomial-time algorithms. In contrast to stochastic programming, distributionally robust optimization explicitly accounts for distributional uncertainty. In this framework, it is assumed that the decision maker has access to only partial distributional information, such as the first- and second-order moments as well as the support. Subsequently, the problem is solved under the worst-case distribution that complies with this partial information. This worst-case approach effectively immunizes the problem against distributional modeling risk. The objective of this thesis is to investigate how robust optimization techniques can be used for quantitative risk management. In particular, we study how the risk of large-scale derivative portfolios can be computed as well as minimized, while making minimal assumptions about the probability distribution of the underlying asset returns. Our interest in derivative portfolios stems from the fact that careless investment in derivatives can yield large losses or even bankruptcy. We show that by employing robust optimization techniques we are able to capture the substantial risks involved in derivative investments. Furthermore, we investigate how distributionally robust chance constrained programs can be reformulated or approximated as tractable optimization problems. Throughout the thesis, we aim to derive tractable models that are scalable to industrial-size problems

Robust utility maximization with intractable claims

We study a continuous-time expected utility maximization problem in which the investor at maturity receives the value of a contingent claim in addition to the investment payoff from the financial market. The investor knows nothing about the claim other than its probability distribution, hence an ``intractable claim''. In view of the lack of necessary information about the claim, we consider a robust formulation to maximize her utility in the worst scenario. We apply the quantile formulation to solve the problem, expressing the quantile function of the optimal terminal investment income as the solution of certain variational inequalities of ordinary differential equations. In the case of an exponential utility, the problem reduces to a (non-robust) rank--dependent utility maximization with probability distortion whose solution is available in the literature