This edited volume collects and unifies a number of recent advances in the signal-processing and machine-learning literature with significant applications in financial risk and portfolio management. The topics in the volume include characterizing statistical dependence and correlation in high dimensions, constructing effective and robust risk measures, and using these notions of risk in portfolio optimization and rebalancing through the lens of convex optimization. It also presents signal-processing approaches to model return, momentum, and mean reversion, including both theoretical and implementation aspects. Modern finance has become global and highly interconnected. Hence, these topics are of great importance in portfolio management and trading, where the financial industry is forced to deal with large and diverse portfolios in a variety of asset classes. The investment universe now includes tens of thousands of international equities and corporate bonds, and a wide variety of other interest rate and derivative products-often with limited, sparse, and noisy market data.

Using traditional risk measures and return forecasting (such as historical sample covariance and sample means in Markowitz theory) in high-dimensional settings is fraught with peril for portfolio optimization, as widely recognized by practitioners. Tools from high-dimensional statistics, such as factor models, eigen-analysis, and various forms of regularization that are widely used in real-time risk ...

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