**TEST PROBLEMS: RISK MANAGEMENT, FINANCIAL ENGINEERING, ADVANCED STATISTICS, LOGISTICS, and MEDICAL APPLICATIONS. The test problems include problem statements, data, and calculation results. **

Research is focused on Financial Engineering Applications: portfolio optimization, asset and liability management (ALM), trading strategies, credit cards scoring, credit rating, derivatives pricing), Structured Finance (collateralized debt obligation (CDO), convertible bonds, mortgage backed securities); Risk Management (optimization of tail risk, Value-at-Risk (VaR), Conditional Value-at-Risk (CVaR), Expected Shortfall, Credit Risk, Drawdown, option pricing) and military applications.

# Research

- Financial Engineering Case Studies (Portfolio Optimization Replication, Hedging, VaR, CVaR, Drawdown, CDaR, Probability, Credit Risk, Cash Matching, Options, Structuring CDO, Mortgage)
- Case Study: Basic CVaR Optimization Problem, Beyond Black-Litterman
- Case Study: Calibrating Risk Preferences
- Case Study: Cash Matching Bond Portfolio
- Case Study: Cash Matching with bPOE and CVaR Functions
- Case Study: Checkerboard Copula Defined by Sperman Rho Coefficients (entropyr)
- Case Study: Checkerboard Copula Defined by Sums of Random Variables
- Case Study: CoCVaR Approach – Risk Contribution Measurement
- Case Study: Convex-Concave-Convex Distributions in Application to CDO Pricing
- Case Study: Estimation of CVaR through Explanatory Factors with CVaR (Superquantile) Regression
- Case Study: Estimation of CVaR through Explanatory Factors with Mixed Quantile Regression
- Case Study: Hedging Portfolio of Options
- CASE STUDY: Maximization of Log-Lokelihood in Hidden Markov Model (hmm_discrete, hmm_normal, linear, linearmulti)
- Case Study: Mortgage Pipeline Hedging
- Case Study: Omega Portfolio Rebalancing
- Case Study: Optimal Hedging of CDO Book
- Case Study: Optimal Position Liquidation with CVaR Constraints
- Case Study: Portfolio Credit-Risk Optimization Modeled by Scenarios and Mixtures of Normal Distributions
- Case Study: Portfolio Management with Basel Accord
- Case Study: Portfolio Optimization with Drawdown Constraints on a Single Path
- Case Study: Portfolio Optimization with Drawdown Constraints on Multiple Paths
- Case Study: Portfolio Optimization with Drawdown Constraints, Single Path vs Multiple Paths
- Case study: Portfolio Optimization with Expectiles
- Case Study: Portfolio Optimization with Exponential, Logarithmic, and Linear-Quadratic Utilities
- Case Study: Portfolio Optimization with Mixed CVaR and Mixed VaR Profiles
- Case Study: Portfolio Optimization with Nonlinear Transaction Costs
- Case Study: Portfolio Optimization with Probabilistic Constraint and Fixed and Proportional Transaction Costs
- Case Study: Portfolio Optimization with Second-Order Stochastic Dominance Constraints
- Case Study: Portfolio Optimization, CVaR vs. ST_DEV
- Case Study: Portfolio Replication with Cardinality and Buyin Constraints
- Case Study: Portfolio Replication with Risk Constraint
- Case Study: Project Selection
- Case Study: Relative Entropy Minimization
- Case Study: Retirement Portfolio Selection
- Case Study: Structuring step up CDO
- Case Study: Style Classification with Quantile Regression
- Case Study: VaR Optimization Retail Portfolio of Bonds
- Case Study: VaR vs Probability Constraints
- Classification in Loan Application Process

- Application Area: Advanced Statistics
- Case Study: Approximation of a Discrete Distribution by other Discrete Distribution Using CVaR Distance
- Case Study: Approximation of a Discrete Distribution by Some Other Discrete Distribution in Euclidean Space by Minimizing Kantorovich-Rubinstein Distance (linear, sqrt_quadratic)
- Case Study: Buffered Neyman-Pearson Classification with Spline-based Feature Transforms
- Case Study: Classification by Buffered AUC (bAUC) Maximization
- Case Study: Classification by Maximizing Area Under ROC Curve (AUC)
- Case Study: CVaR Norm Regression
- Case Study: Data Envelopment Analysis
- Case Study: Data Envelopment Analysis, Stochastic Case, Buffered-Ranking
- Case Study: Distribution Approximation by Maximizing Entropy with Second-Order Stochastic Dominance and Moment Constraints
- Case Study: Estimating Probability Distributions with Quantile Regression
- Case Study: Fitting mixture models with CVaR constraints
- Case Study: Linear Regression in Tranche
- Case Study: Logistic Regression and Regularized Logistics Regression Applied to Estimating the Probability of Cesarean Section
- Case Study: Minimization of Kantorovich-Rubinstein distance between two distributions (kantor, ksm_avg, cardn, linear)
- Case Study: Parameter Estimation of Generalized Pareto Distribution
- Case Study: Projection on Polyhedron with Various Norms
- Case Study: Sparse Reconstruction Problems from SPARCO Toolbox
- Case Study: Sparse Reconstruction Problems from SPARCO toolbox in PSG MATLAB Environment (fnext)
- Case Study: Sparse Signal Reconstruction: a Cardinality Approach
- Case Study: Spline Approximation
- Case Study: Spline Regression
- Case Study: Support Vector Machines Based on Tail Risk Measures
- Case Study: Value-at-Risk Support Vector Machine (Var-SVM)

- Application Area: Stochastic Programming
- Application Area: Logistics
- Case Study: Cell Towers allocation with Probability of Exceedance and VaR functions
- Case Study: Optimal Allocation of Stock Levels and Stochastic Customer Demands to a Capacitated Resource
- Case Study: Optimal Crop Production and Insurance Coverage
- Case Study: Optimal Tests Selection
- Case Study: Production Planning
- Case Study: Shortest Path in a Stochastic Weighted Graph using Average, bPOE, and CVaR
- Case Study: Shortest Path in a Stochastic Weighted Graph using Average, CVaR, POE and bPOE Performance Functions
- Case Study: Stochastic Multicommodity Network Flow Problem
- Case Study: Travelling Salesman
- Network Optimization by Minimization of Cardinality of Upper Average (CUA)

- Application Area: Medical Applications
- Application Area: Numerical Mathematics
- List of Functions