Session 22. Multivariate stochastic modelling in finance, insurance and risk management

Time-consistency for dynamic risk and performance measures

Marcin Pitera, Faculty of Mathematics and Computer Science, Jagiellonian University, Poland
The talk is based on the joint work with T.R. Bielecki and I. Cialenco.
A new definition of time-consistency for dynamic local and monotone measures (LM-measures) is proposed. The definition applies to both dynamic monetary risk measures [4] as well as dynamic measures of performance [2,3]. Our definition is based on information update procedure, rather than on a benchmark set of financial positions, as was done in [1]. This allows for a more flexible approach to studying time consistency. Connection with definitions of time consistency existing in the literature are discussed, as well as some basic properties of updating procedures.
References
  1. B. Acciaio, I. Penner, Dynamic risk measures , Advanced Mathematical Methods for Finance (2011), 1--34 (G. Di Nunno and B. Öksendal Eds.).
  2. T. R. Bielecki, I. Cialenco, M. Pitera, Dynamic limit growth indices in discrete time , arXiv preprint arXiv:1312.1006 (2013).
  3. T. R. Bielecki, I. Cialenco, Z. Zhang, Dynamic coherent acceptability indices and their applications to finance , Mathematical Finance (2012).
  4. P. Cheridito, F. Delbaen, and M. Kupper, Dynamic monetary risk measures for bounded discrete-time processes , Electron. J. Probab. 11 (2006), no. 3, 57-106.
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