A PDE approach to risk measures of derivatives

Tak Kuen Siu, Hailiang Yang

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


This paper proposes a partial differential equation (PDE) approach to calculate coherent risk measures for portfolios of derivatives under the Black-Scholes economy. It enables us to define the risk measures in a dynamic way and to deal with American options in a relatively effective way. Our risk measure is based on the representation form of coherent risk measures. Through the use of some earlier results the PDE satisfied by the risk measures are derived. The PDE resembles the standard Black-Scholes type PDE which can be solved using standard techniques from the mathematical finance literature. Indeed, these results reveal that the PDE approach can provide practitioners with a more applicable and flexible way to implement coherent risk measures for derivatives in the context of the Black-Scholes model.

Original languageEnglish
Pages (from-to)211-228
Number of pages18
JournalApplied Mathematical Finance
Issue number3
Publication statusPublished - 1 Jan 2000
Externally publishedYes


  • coherent risk measures
  • American options
  • physical probability measure
  • subjective probability measures
  • transaction costs


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