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Case Studies with PSG

Contents

Case Studies in Run-File and MATLAB PSG Environments.

Hedging Portfolio of Options	Hedges a Portfolio of Options by a Portfolio of Stocks and Options.
Mortgage Pipeline Hedging	Investigates the optimal pipeline hedging strategy.
Omega Portfolio Rebalancing	Demonstrates an Omega optimization setup for a portfolio optimization problem. A fund of funds blends the risk-return profiles of various hedge fund managers/strategies to meet investor requirements.
Optimal Crop Production and Insurance Coverage	Investigates an optimal crop production and insurance coverage under three types of risk constraints: CVaR, VaR, and Probability Exceeding Penalty constraint.
Optimal Hedging of CDO Book	Demonstrates a portfolio of Credit Default Swaps (CDS) and Credit Indices that hedge against changes in a CDO (Collateralized Debt Obligation) book.
Optimal Tests Selection	Considers the problem of optimal selection of tests subject to several constraints on available resources (e.g. money, times, and people).
Optimization Beyond Black Litterman	Demonstrates a simple (basic) setup of single-period portfolio optimization problem when risk is measured by CVaR.
Optimization Retail Portfolio of Bonds	This case study is conducted with the portfolio retail loans dataset provided by the Kukmin Bank, Korea.
Portfolio Management with Basel Accord	Demonstrates an optimization setup for credit portfolio management.
Portfolio Optimization with Drawdown Constraints on a Single Path	Demonstrates an optimization setup with Conditional Drawdown-at-Risk (CDaR) deviation on a single sample path.
Portfolio Optimization with Drawdown Constraints on Multiple Paths	Demonstrates an optimization setup with Conditional Drawdown-at-Risk (CDaR) deviation with multiple sample paths.
Portfolio Optimization with Drawdown Constraints, Single Path vs Multiple Paths	Compares solutions of two optimization problems: (1) maximizing annualized portfolio return on multiple sample paths subject to constraint on CDaR Deviation Multiple and (2) maximizing annualized portfolio return on a single sample path subject to constraint on CDaR Deviation.
Portfolio Optimization with Exponential, Logarithmic, and Linear-Quadratic Utilities	Compares the optimal decision generated by the Exponential utility function with that generated by the Linear-Quadratic utility function.
Portfolio Optimization with Nonlinear Transaction Costs	Considers portfolio optimization problem with the average gain objective function, CVaR constraint, and nonlinear transaction cost depending upon the total dollar value of the bought/sold assets.
Portfolio Optimization with Second Orders Stochastic Dominance Constraints	Considers portfolio optimization problem with the average gain objective function, CVaR constraint, and nonlinearThis case study finds a portfolio with return dominating the benchmark portfolio return in the second order and having maximum expected return.
Portfolio Optimization, CVaR vs Standard Deviation	Compares three setups of a single-period portfolio optimization problem when risk is measured by CVaR Deviation, Standard Deviation calculated with the matrix of scenarios, and Standard Deviation calculated with the covariance matrix.
Portfolio Replication with Risk Constraint	Demonstrates three settings for a portfolio replication problem with the replication error measured by Mean Absolute Penalty. Underperformance of the portfolio compared to S&P100 index is measures by CVaR. Distribution of residuals is shaped with a CVaR constraint (several constraints can be specified, if of interest).
Project Selection	Demonstrates an optimization setup for a project selection problem. Each project, if chosen, requires an initial capital outlay. Projects are selected to maximize the net present value of the investment subject to constraint on the initial available capital.
Relative Entropy Minimization	Demonstrates optimization problem minimizing Relative Entropy under linear constraints using the riskprog subroutine.
Stochastic Utility Problem	Solves Stochastic Utility (or Expected Utility) problem which is approximated by sampling stochastic parameters of this problem (Sampling Average Approximation approach).
Structuring Step-up CDO	Demonstrates two optimization setups for determining attachment points in step-up Collateralized Debt Obligation (CDO).
Style Classification with Quantile Regression	Applies percentile regression to the return-based style classification of a mutual fund.
Binary Classification with Splines	Demonstrate binary classifier on the base of approximation multidimensional data (with several independent variables) by a sum of splines using PSG function spline_sum.
Logistic Regression and Regularized Logistics Regression Applied to Estimating Probabilities	Demonstrates three optimization formulations of the logistic regression problem: 1) Maximization of the log-likelihood function (“plain vanilla” logistic regression); 2) Maximization of the log-likelihood function minus additional regularization term (regularized logistic regression); 3) Maximization of the log-likelihood function with cardinality constraints. Cross-Validation technique is used.
Mixed Quantile Regression: Estimation of CVaR with Explanatory Factors	Considers Mixed Percentile Regression for the estimation of Conditional Value-at-Risk (CVaR) of return distribution of a mutual fund. The estimated coefficients represent the fund’s style with respect to some indices, and therefore the procedure is called “style classification.”
Quantile Regression: Style Classification of Portfolio	Demonstrates percentile regression for the return-based style classification of a mutual fund. The procedure regresses fund return by several indices as explanatory variables. The estimated coefficients represent the fund’s loads on the indices.
Intensity-Modulated Radiation Therapy Treatment Planning Problem	Solves an intensity-modulated radiation therapy (IMRT) treatment planning problem.
VaR vs Probability Constraints	Demonstrates two portfolio optimization problems. In both cases the estimated return of a portfolio is maximized. In the first problem, a constraint on probability is imposed; in the second problem, an equivalent constraint on VaR is imposed.
Investment Strategies for Portfolio of Hedge Funds	Investigates two investment strategies for a portfolio of hedge funds.The first strategy rebalances the portfolio by solving an optimization problem. The second strategy, called "20-best", every time period selects 20 hedge funds with the highest return (over available data) and give them equal weights.
Logistic Regression with Factors Transformed by Splines and Approaches for Dimension Reduction	This case study demonstrates binary classification with a large number of factors (independent variables). Classification algorithm is based on the Logistic Regression (LR) and includes four main steps: Step 1) Factors are transformed by spline approximation using maximum likelihood in LR. Step 2) Removing factors with a small importance (increment) using maximum likelihood in LR. Step 3) Removing factors by adding cardinality constraint to LR optimization problem.Step 4) Model verification with 4-fold cross-validation.
Supply Chain Planning Problem	This case study models the supply chain design problem as a sequence of splitting and combining processes. The problem is formulated as a two-stage stochastic program. The first-stage decisions are strategic location decisions, whereas the second stage consists of operational decisions. The objective is to maximize the expected profits over the planning horizon. Another variant of objective is to minimize the sum of investment costs and expected costs of operating the supply chain. Below we give a general formulation of the problem. It is reformulated as minimization one. Solutions of the second stage problem for different scenarios give the values of the stochastic Recourse Function.