### Abstract

We develop an approach to time-consistent risk control of continuous-time processes in Markov systems with finite state space. Our analysis is based on time-consistent risk evaluation in continuous time, which uses the dual representation of dynamic coherent risk measures. Introducing a suitable differentiability concept for multivalued mappings and a concept of strong time consistency, we approximate the risk multikernels of the Markov system via set-valued derivatives, which gives rise to the concept of a risk multigenerator of a Markov process. We focus on risk-averse Markov decision problems with cost evaluated at the terminal state. We derive a system of ordinary differential equations for the risk evaluation of a given policy, which generalize the classical backward Kolmogorov equations for Markov processes. Furthermore, we establish optimality conditions in form of differential equation involving the support function of the risk multigenerator and we identify conditions for the existence of an optimal Markov policy.

Original language | English (US) |
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Title of host publication | Proceedings of the SIAM Conference on Control and Its Applications, CT 2017 |

Publisher | Society for Industrial and Applied Mathematics Publications |

Pages | 78-85 |

Number of pages | 8 |

ISBN (Electronic) | 9781611975000 |

State | Published - Jan 1 2017 |

Event | 2017 SIAM Conference on Control and Its Applications, CT 2017 - Pittsburgh, United States Duration: Jul 10 2017 → Jul 12 2017 |

### Other

Other | 2017 SIAM Conference on Control and Its Applications, CT 2017 |
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Country | United States |

City | Pittsburgh |

Period | 7/10/17 → 7/12/17 |

### All Science Journal Classification (ASJC) codes

- Control and Systems Engineering

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## Cite this

*Proceedings of the SIAM Conference on Control and Its Applications, CT 2017*(pp. 78-85). Society for Industrial and Applied Mathematics Publications.