The diversified strategy can reduce the systematic risk efficiently, but may fail to account for emergent and default risk that many decision-makers usually face at large-scale level. Modern data-driven methodologies allow optimizing both systematic and non-systematic risks in a unified framework. In this article, we demonstrate an approach to analyze and compare partial-diversified portfolios of Credit Default Swap. We classify and investigate different metrics of credit risks and integrate them with limited diversification and other performance objectives. We test the developed approach in a study of hundreds of business contract investments over the recent financial crisis. The results indicate that the decisions using limited diversification are more robust in terms of allocation structure and out-of-sample downside risks reduction. Therefore, the partial-diversified optimization models provide alternatives to support a variety of problems involving unknown risks.

Tracking the movement of an index involves the parameter learning from data and algorithm design for solving the decision model. In this paper, we present a factor induced robust index tracking model to protect against the parameter estimation error and immunize both systematic and default risks of tracking portfolios. A Lagrangian-based algorithm is applied to approximate optimal solutions and enhance the capacity of the decision model. Two types of inequalities are derived to strengthen the Lagrangian lower bound and speed up the whole Lagrangian Relaxation (LR) method. With the designed system, we investigate large Credit Default Swap (CDS) dataset that includes 1246 daily observations across near 500 individual contracts. We show that the fluctuation range of portfolio out-of-sample returns can be shrunk significantly by using the proposed robust counterpart, e.g. from [-12%, 12%] to [-4%, 4%] in the second half of 2013, and other comparison metrics such as Sharpe ratio and tracking error to transaction costs (TE/TC) ratio could also be consistently improved.

This paper describes a cardinality constrained network flow structure whose special characteristics are used to analyse different risk aspects under an environment of uncertainty. The network structure developed is a suitable alternative to support financial planning and many other decision-making problems with limited resources. By setting a diversification level, we can manage systematic and non-systematic risks under a stochastic mixed integer linear programming framework. A dual decomposition method, Progressive Hedging (PH), is applied to more efficiently accommodate instances with large numbers of scenarios. We studied the impact of the level of the diversification on transaction costs and considered different factors that influence the performance of the algorithm. In particular, a Lagrangian bound is embedded to enhance the capacity of the method. Numerical results show the effectiveness of the proposed decision support approach.

We construct portfolios from the credit default swap (CDS) market by incorporating cardinality and solvency constraints into mean-variance and conditional value at risk (CVaR) models. Cardinality constraints are applied to limit the portfolio size and improve the allocation structure, while the solvency constraint is used to insulate the default risks of the portfolios under worst scenarios. CDS-based portfolios involve uncertainties that stem from spread changing and jump-to-default volatilities. We show that these uncertainties can be identified and managed using our developed systematic approach. Market data analysis from the CDS portfolios shows that using cardinality constraints reduces counterparty risks significantly. The proposed cardinality constrained CVaR model has robust performance in terms of the portfolio Sharpe ratio and one other metric, and also generally outperforms the associated mean-variance strategy.

After 2007-2008 crisis, it is clear that corporate credit scoring is becoming a key role in credit risk management. In this paper, we investigate the performances of credit scoring models applied to CDS data sets. The classification performance of deep learning algorithm such as deep belief networks with Restricted Boltzmann Machines are evaluated and compared with some popular credit scoring models such as logistic regression, multi-layer perceptron and support vector machine. The performance is assessed using the classification accuracy and the area under the receiver operating characteristic curve. It is found that DBN yields the best performance.

We transformed a data envelopment analysis (DEA) optimization model into a robust second-order cone equivalent to immunize against output perturbation in an uncertainty set. The robust DEA framework was then used to assess the effect of a wood hardening treatment using methyl methacrylate (MMA) on selected hybrid poplar clones. Because the performance of MMA-hardened hybrid poplar clones varies across clones, ranking hardened clones is crucial for developing hardening treatments for specific industrial applications. The numerical results demonstrate that the hardening treatment can be optimized by applying the proposed DEA framework to select the best hybrid poplar clone types and the optimal amount of impregnated chemicals.

We address asset classification and portfolio selection in this paper. Surprisingly, money managers find that the market volatility becomes more frequent as more advanced innovations are applied in the financial system. For example, the high-frequency trading may amplify the deviation on U.S. stock market [1], [2]. Therefore, a reliable method to appraise the asset performance is extremely important to portfolio managers, regulators, and individual investors. One alternative approach to achieve this goal is data envelopment analysis (DEA). Asset performance was ranked from both self-and peer-evaluation perspectives. Specifically, we extended the cross-efficiency analysis in DEA that uses row and column means to portfolio selection and identify different types of asset set. This classification process can help investors to construct a more robust portfolio. Numerical experiments based on S&P500 showed that the portfolio with cross-efficiency analysis can generate better Sharpe ratios during the period of financial crisis in 2008.