### Abstract

We consider a stochastic model of changes of prices in real estate markets. We suppose that in a book of prices the changes happen in points of jumps of a Poisson process with a random intensity, i.e. moments of changes sequently follow to a random process of the Cox process type. We calculate cumulative mathematical expectations and variances for the random intensity of this point process. In the case that the process of random intensity is a martingale the cumulative variance has a linear grows. We statistically process a number of observations of real estate prices and accept hypotheses of a linear grows for estimations as well for cumulative average, as for cumulative variance both for input and output prises that are writing in the book of prises.

Original language | English |
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Title of host publication | Applied Mathematics and Computer Science |

Subtitle of host publication | Proceedings of the 1st International Conference on Applied Mathematics and Computer Science |

Publisher | American Institute of Physics |

Volume | 1836 |

ISBN (Electronic) | 9780735415065 |

DOIs | |

State | Published - 5 Jun 2017 |

Event | 1st International Conference on Applied Mathematics and Computer Science, ICAMCS 2017 - Rome, Italy Duration: 26 Jan 2017 → 28 Jan 2017 |

### Conference

Conference | 1st International Conference on Applied Mathematics and Computer Science, ICAMCS 2017 |
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Country | Italy |

City | Rome |

Period | 26/01/17 → 28/01/17 |

### Keywords

- Double Stochastic Poisson Process
- dynamics of prices in real estate markets
- Gamma Lévy process
- random intensity

### Scopus subject areas

- Physics and Astronomy(all)
- Mathematics(all)
- Decision Sciences(all)

### Cite this

*Applied Mathematics and Computer Science: Proceedings of the 1st International Conference on Applied Mathematics and Computer Science*(Vol. 1836). [020087] American Institute of Physics. https://doi.org/10.1063/1.4982027

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*Applied Mathematics and Computer Science: Proceedings of the 1st International Conference on Applied Mathematics and Computer Science.*vol. 1836, 020087, American Institute of Physics, 1st International Conference on Applied Mathematics and Computer Science, ICAMCS 2017, Rome, Italy, 26/01/17. https://doi.org/10.1063/1.4982027

**A stochastic model for stationary dynamics of prices in real estate markets. A case of random intensity for Poisson moments of prices changes.** / Rusakov, Oleg; Laskin, Michael.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review

TY - GEN

T1 - A stochastic model for stationary dynamics of prices in real estate markets. A case of random intensity for Poisson moments of prices changes

AU - Rusakov, Oleg

AU - Laskin, Michael

PY - 2017/6/5

Y1 - 2017/6/5

N2 - We consider a stochastic model of changes of prices in real estate markets. We suppose that in a book of prices the changes happen in points of jumps of a Poisson process with a random intensity, i.e. moments of changes sequently follow to a random process of the Cox process type. We calculate cumulative mathematical expectations and variances for the random intensity of this point process. In the case that the process of random intensity is a martingale the cumulative variance has a linear grows. We statistically process a number of observations of real estate prices and accept hypotheses of a linear grows for estimations as well for cumulative average, as for cumulative variance both for input and output prises that are writing in the book of prises.

AB - We consider a stochastic model of changes of prices in real estate markets. We suppose that in a book of prices the changes happen in points of jumps of a Poisson process with a random intensity, i.e. moments of changes sequently follow to a random process of the Cox process type. We calculate cumulative mathematical expectations and variances for the random intensity of this point process. In the case that the process of random intensity is a martingale the cumulative variance has a linear grows. We statistically process a number of observations of real estate prices and accept hypotheses of a linear grows for estimations as well for cumulative average, as for cumulative variance both for input and output prises that are writing in the book of prises.

KW - Double Stochastic Poisson Process

KW - dynamics of prices in real estate markets

KW - Gamma Lévy process

KW - random intensity

UR - http://www.scopus.com/inward/record.url?scp=85021372216&partnerID=8YFLogxK

U2 - 10.1063/1.4982027

DO - 10.1063/1.4982027

M3 - Conference contribution

VL - 1836

BT - Applied Mathematics and Computer Science

PB - American Institute of Physics

ER -