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BUDGET ALLOCATIONS IN OPERATIONAL RISK MANAGEMENT

Published online by Cambridge University Press:  11 July 2017

Yuqian Xu ,
Jiawei Zhang  and
Michael Pinedo
Yuqian Xu
Affiliation:
College of Business, University of Illinois at Urbana-Champaign, Champaign, IL 61820, USA E-mail: [email protected]
Jiawei Zhang
Affiliation:
Stern Business School, New York University, New York, NY 10012, USA E-mail: [email protected]; [email protected]
Michael Pinedo
Affiliation:
Stern Business School, New York University, New York, NY 10012, USA E-mail: [email protected]; [email protected]
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Abstract

We consider a resource allocation model to analyze investment strategies for financial services firms in order to minimize their operational risk losses. A firm has to decide how much to invest in human resources and in infrastructure (information technology). The operational risk losses are a function of the activity level of the firm, of the amounts invested in personnel and in infrastructure, and of interaction effects between the amounts invested in personnel and infrastructure. We first consider a deterministic setting and show certain monotonicity properties of the optimal investments assuming general loss functions that are convex. We find that because of the interaction effects “economies of scale" may not hold in our setting, in contrast to a typical manufacturing environment. We then consider a general polynomial loss function in a stochastic setting with the number of transactions at the firm being a random variable. We characterize the asymptotic behaviors of the optimal investments in both heavy and light trading environments. We show that when the market is very liquid, that is, it is subject to heavy transaction volumes, it is optimal for a financial firm that is highly risk sensitive to use a balanced investment strategy. Both a heavier right tail of the distribution of transaction volume and a firm's risk sensitivity necessitate larger investments; in a heavy trading environment these two factors reinforce one another. However, in a light trading environment with the transaction volume having a heavy left tail the investment will be independent of the firm's sensitivity to risk.

Keywords

asymptoticconvexityheavy tailoperational riskrisk sensitivitystochastic resource allocation
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 32 , Issue 3 , July 2018 , pp. 434 - 459
Copyright
Copyright © Cambridge University Press 2017 

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References

1.Basel Committee on Banking Supervision (2006). The first pillar-minimum capital requirements. BIS consultative document.Google Scholar
2.Basel Committee on Banking Supervision (2011). Principles for the sound management of operational risk. BIS consultative document.Google Scholar
3.Bish, E.K. & Wang, Q. (2004). Optimal investment strategies for flexible resources, considering pricing and correlated demands. Operations Research 52(6): 954–964.Google Scholar
4.Bish, E.K., Zeng, X., Liu, J., & Bish, D.R. (2012). Comparative statics analysis of multiproduct newsvendor networks under responsive pricing. Operations Research 60(5): 1111–1124.Google Scholar
5.Black, F. & Litterman, R. (1992). Global portfolio optimization. Financial Analysts Journal 48(5): 28–43.Google Scholar
6.Bocker, K. & Kluppelberg, C. (2005). Operational VaR: a closed-form approximation. Risk Magazine 18(12): 90–93.Google Scholar
7.Boudreau, J.W. (2004). Organizational behavior, strategy, performance, and design in management science. Management Science 50(11): 1463–1476.Google Scholar
8.Boudreau, J.W., Hopp, W., McClain, J.O., & Thomas, L.J. (2003). On the interface between operations and human resources management. Manufacturing and Services Operations Management 5(3): 179–202.Google Scholar
9.Cassenti, D.N., Kelley, T.D., & Carlson, R.A. (2010). Modeling the workload-performance relationship. Proceedings of the Human Factors and Ergonomics Society Annual Meeting 54(19): 1684–1688.Google Scholar
10.Chapelle, A., Crama, Y., Hübner, G., & Peters, J.P. (2008). Practical methods for measuring and managing operational risk in the financial sector: a clinical study. Journal of Banking and Finance 32(6): 1049–1061.Google Scholar
11.Cheng, F., Gamarnik, D., Jengte, N., Min, W., & Ramachandran, B. (2007). Modeling operational risks in business processes. Journal of Operational Risk 2(2): 73–98.Google Scholar
12.Chernobai, A.S., Rachev, S.T., & Fabozzi, F.J. (2007). Operational risk: A guide to Basel II capital requirements, models, and analysis. New York: John Wiley and Sons.Google Scholar
13.Chod, J. & Rudi, N. (2005). Resource flexibility with responsive pricing. Operations Research 53(3): 532–548.Google Scholar
14.Cooper, W.L. (2002). Asymptotic behavior of an allocation policy for revenue management. Operations Research 50(4): 720–727.Google Scholar
15.Cruz, M.G. (2002). Modeling, measuring and hedging operational risk. New York: John Wiley and Sons.Google Scholar
16.Deloitte (2013). Directors, CFOs Share Views on Risk, but Diverge on Time Spent. http://deloitte.wsj.com/riskandcompliance/2013/04/16/.Google Scholar
17.Gregoriou, G.N. (2009). Operational risk toward basel III: Best practices and issues in modeling, management, and regulation. New York: John Wiley and Sons.Google Scholar
18.Hora, M. & Klassen, R.D. (2013). Learning from others’ misfortune: factors influencing knowledge acquisition to reduce operational risk. Journal of Operations Management 31(1): 52–61.Google Scholar
19.Iyer, R.K. & Rossetti, D.J. (1986). A measurement-based model for workload dependence of cpu errors. IEEE Transactions on Computers 100(6): 511–519.Google Scholar
20.Jarrow, R.A. (2008). Operational risk. Journal of Banking and Finance 32(5): 870–879.Google Scholar
21.Jarrow, R.A., Oxman, J., & Yildirim, Y. (2010). The cost of operational risk loss insurance. Review of Derivatives Research 13(3): 273–295.Google Scholar
22.Karger, D.R., Oh, S., & Shah, D. (2014). Budget-optimal task allocation for reliable crowdsourcing systems. Operations Research 62(1): 1–24.Google Scholar
23.Karsten, F., Slikker, M., & Van Houtum, G.J. (2015). Resource pooling and cost allocation among independent service providers. Operations Research 62(2): 476–488.Google Scholar
24.Kc, D.S. & Terwiesch, C. (2009). Impact of workload on service time and patient safety: An econometric analysis of hospital operations. Management Science 55(9): 1486–1498.Google Scholar
25.Kuntz, L., Mennicken, R., & Scholtes, S. (2014). Stress on the ward: Evidence of safety tipping points in hospitals. Management Science 64(1): 754–771.Google Scholar
26.Leippold, M. & Vanini, P. (2005). The quantification of operational risk. Journal of Risk 8(1): 59–85.Google Scholar
27.Luss, H. (2012). Equitable resource allocation: Models, algorithms, and applications. New York: John Wiley and Sons.Google Scholar
28.Markowitz, H. (1952). Portfolio selection. The Journal of Finance 7(1): 77–91.Google Scholar
29.Meier, H., Christofides, N., & Salkin, G. (2001). Capital budgeting under uncertainty-an integrated approach using contingent claims analysis and integer programming. Operations Research 49(2): 196–206.Google Scholar
30.Nash, P. & Gittins, J.C. (1977). A hamiltonian approach to optimal stochastic resource allocation. Advances in Applied Probability 9(1): 55–68.Google Scholar
31.Neil, M., Fenton, N., & Tailor, M. (2005). Using Bayesian networks to model expected and unexpected operational losses. Risk Analysis 25(4): 963–972.Google Scholar
32.Powell, A., Savin, S., & Savva, N. (2012). Physician workload and hospital reimbursement: Overworked physicians generate less revenue per patient. Manufacturing and Services Operations Management 14(4): 512–528.Google Scholar
33.Ross, S.M. & Wu, D.T. (2013). A generalized coupon collecting model as a parsimonious optimal stochastic assignment model. Annals of Operations Research 208(1): 133–146.Google Scholar
34.Royset, J.O. & Szechtman, R. (2013). Optimal budget allocation for sample average approximation. Operations Research 61(3): 762–776.Google Scholar
35.Scharfman, J.A. (2008). Hedge fund operational due diligence: Understanding the risks. New York: John Wiley and Sons.Google Scholar
36.Sparrow, A. (2000). A theoretical framework for operational risk management and opportunity realisation. No. 00/10 New Zealand Treasury.Google Scholar
37.Tan, T.F. & Netessine, S. (2014). When does the devil make work? An empirical study of the impact of workload on worker productivity. Management Science 60(6): 1574–1593.Google Scholar
38.Thomas, P., Teneketzis, D., & Mackie-Mason, J.K. (2002). A market-based approach to optimal resource allocation in integrated-services connection-oriented networks. Operations Research 50(4): 603–616.Google Scholar
39.Topkis, D.M. (2011). Supermodularity and complementarity. Princeton, NJ: Princeton University Press.Google Scholar
40.Van Mieghem, J.A. (2003). Capacity management, investment, and hedging: Review and recent developments. Manufacturing and Services Operations Management 5(4): 269–302.Google Scholar
41.Van Mieghem, J.A. & Dada, M. (1999). Price versus production postponement: capacity and competition. Management Science 45(12): 1639–1649.Google Scholar
42.Wu, D.T. & Ross, S.M. (2015). A stochastic assignment problem. Naval Research Logistics (NRL) 62(1): 23–31.Google Scholar
43.Xu, Y., Pinedo, M., & Xue, M. (2017). Operational risk in financial services: A review and new research opportunities. Production and Operations Management 26(3): 426–445.Google Scholar