A functional Ito's calculus approach to convex risk measures with jump diffusion

Tak Kuen Siu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


Convex risk measures for European contingent claims are studied in a non-Markovian jump-diffusion modeling framework using functional Itô's calculus. Two representations for a convex risk measure are considered, one based on a nonlinear g-expectation and another one based on a representation theorem. Functional Itô's calculus for càdlàg processes, backward stochastic differential equations (BSDEs) with jumps and stochastic optimal control theory are used to discuss the evaluation of convex risk measures. FPDIEs and PDIEs for convex risk measures are derived in the Markovian and non-Markovian situations, respectively. An entropic risk measure, which is a particular case of a convex risk measure, is discussed.

Original languageEnglish
Pages (from-to)874-883
Number of pages10
JournalEuropean Journal of Operational Research
Issue number3
Publication statusPublished - 1 May 2016


  • Convex risk measure
  • Entropic risk measure
  • Functional Itô's calculus
  • Non-Markovian jump-diffusion model
  • Risk management


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