### Abstract

We consider a class of problems concerned with maximizing probabilities, given stage-wise targets, which generalizes the standard threshold probability problem in Markov decision processes. The objective function is the probability that, at all stages, the associatively combined accumulation of rewards earned up to that point takes its value in a specified stage-wise interval. It is shown that this class reduces to the case of the nonnegative-valued multiplicative criterion through an invariant imbedding technique. We derive a recursive formula for the optimal value function and an effective method for obtaining the optimal policies.

Original language | English |
---|---|

Pages (from-to) | 461-472 |

Number of pages | 12 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 386 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2012 Feb 1 |

### Keywords

- Dynamic programming
- Liquidity risk
- Markov decision process
- Nonnegative-valued multiplicative criterion
- Threshold probability

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

## Fingerprint Dive into the research topics of 'Threshold probability of non-terminal type in finite horizon Markov decision processes'. Together they form a unique fingerprint.

## Cite this

Kira, A., Ueno, T., & Fujita, T. (2012). Threshold probability of non-terminal type in finite horizon Markov decision processes.

*Journal of Mathematical Analysis and Applications*,*386*(1), 461-472. https://doi.org/10.1016/j.jmaa.2011.08.006