Budget allocations in operational risk management

Yuqian Xu, Jiawei Zhang, Michael Pinedo

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)434-459
Number of pages26
JournalProbability in the Engineering and Informational Sciences
Issue number3
StatePublished - Jul 1 2018


  • Key wordsasymptotic
  • convexity
  • heavy tail
  • operational risk
  • risk sensitivity
  • stochastic resource allocation

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering


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