Portfolio Value-at-Risk Optimization for Asymmetrically Distributed Asset Returns

Joel  Goh; Kian Guan  Lim; Melvyn  Sim; Weina  Zhang

Article | European Journal of Operational Research

Portfolio Value-at-Risk Optimization for Asymmetrically Distributed Asset Returns

by Joel Goh, Kian Guan Lim, Melvyn Sim and Weina Zhang

Abstract

We propose a new approach to portfolio optimization by separating asset return distributions into positive and negative half-spaces. The approach minimizes a newly-defined Partitioned Value-at-Risk (PVaR) risk measure by using half-space statistical information. Using simulated data, the PVaR approach always generates better risk-return tradeoffs in the optimal portfolios when compared to traditional Markowitz mean–variance approach. When using real financial data, our approach also outperforms the Markowitz approach in the risk-return tradeoff. Given that the PVaR measure is also a robust risk measure, our new approach can be very useful for optimal portfolio allocations when asset return distributions are asymmetrical.

Keywords: robust optimization; portfolio management; value-at-risk; Mathematical Methods; Finance;

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Goh, Joel, Kian Guan Lim, Melvyn Sim, and Weina Zhang. "Portfolio Value-at-Risk Optimization for Asymmetrically Distributed Asset Returns." European Journal of Operational Research 221, no. 2 (September 1, 2012): 397–406.

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Article | Operations Research | May–June 2018

Data Uncertainty in Markov Chains: Application to Cost-Effectiveness Analyses of Medical Innovations

Joel Goh, Mohsen Bayati, Stefanos A. Zenios, Sundeep Singh and David Moore

Cost-effectiveness studies of medical innovations often suffer from data inadequacy. When Markov chains are used as a modeling framework for such studies, this data inadequacy can manifest itself as imprecision in the elements of the transition matrix. In this paper, we study how to compute maximal and minimal values for the discounted value of the chain (with respect to a vector of state-wise costs or rewards) as these uncertain transition parameters jointly vary within a given uncertainty set. We show that these problems are computationally tractable if the uncertainty set has a row-wise structure. Conversely, we prove that the row-wise structure is necessary for tractability. Without it, the problems become computationally intractable (strongly NP-hard). We apply our model to assess the cost effectiveness of fecal immunochemical testing (FIT), a new screening method for colorectal cancer. Our results show that despite the large uncertainty in FIT's performance, it could be cost-effective relative to the prevailing screening method of colonoscopy.

Keywords: Markov Chains; cost effectiveness; medical innovations; Colorectal Cancer; Health Care and Treatment; Cost vs Benefits; Innovation and Invention; Mathematical Methods; Health Industry;

Citation:

Goh, Joel, Mohsen Bayati, Stefanos A. Zenios, Sundeep Singh, and David Moore. "Data Uncertainty in Markov Chains: Application to Cost-Effectiveness Analyses of Medical Innovations." Operations Research 66, no. 3 (May–June 2018): 697–715. (Winner, 2014 INFORMS Health Applications Society Pierskalla Award & Finalist, 2014 INFORMS George E. Nicholson student paper competition.) View Details

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In December 2014, Dr. Anthony Furlan, chair of the Department of Neurology at University Hospitals Cleveland Medical Center (UH), faced a mandate from the hospital’s executive leadership team. Specifically, all UH departments were directed to take steps within six months to reduce the waiting time for outpatient appointments—measured as the time to first available outpatient appointment—to no more than 15 days. For Furlan and his colleagues in neurology, achieving this target was a significant challenge, as the department’s current time to first available appointment was 93 days. The case considers several alternatives for reducing waiting time in outpatient neurology without increasing the total clinical staff. The case allows students to evaluate opportunities for expanding the effective capacity of a complex service operation and to understand the tradeoffs between customer service and labor utilization.

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Portfolio Value-at-Risk Optimization for Asymmetrically Distributed Asset Returns

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