Solvency Markov Decision Processes with Interest

D 2013

Solvency Markov Decision Processes with Interest

BRÁZDIL, Tomáš, Taolue CHEN, Vojtěch FOREJT, Petr NOVOTNÝ, Aistis SIMAITIS et. al.

Basic information

Original name

Solvency Markov Decision Processes with Interest

Authors

BRÁZDIL, Tomáš (203 Czech Republic, guarantor, belonging to the institution), Taolue CHEN (156 China), Vojtěch FOREJT (203 Czech Republic, belonging to the institution), Petr NOVOTNÝ (203 Czech Republic, belonging to the institution) and Aistis SIMAITIS (440 Lithuania)

Edition

Dagstuhl, Germany, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013), p. 487-499, 13 pp. 2013

Publisher

IBFI Schloss Dagstuhl

Other information

Language

English

Type of outcome

Stať ve sborníku

Field of Study

10201 Computer sciences, information science, bioinformatics

Country of publisher

Germany

Confidentiality degree

není předmětem státního či obchodního tajemství

Publication form

electronic version available online

References:

URL

RIV identification code

RIV/00216224:14330/13:00066380

Organization unit

Faculty of Informatics

ISBN

978-3-939897-64-4

ISSN

DOI

http://dx.doi.org/10.4230/LIPIcs.FSTTCS.2013.487

Keywords in English

stochastic systems; markov decision processes; reward functions

Abstract

V originále

Solvency games, introduced by Berger et al., provide an abstract framework for modeling decisions of a risk-averse investor, whose goal is to avoid ever going broke. We study a new variant of this model, where in addition to stochastic environment and fixed increments and decrements to the investor's wealth we introduce interest, which is earned or paid on the current level of savings or debt, respectively. We concentrate on problems related to the minimum initial wealth sufficient to avoid bankrupting (i.e. steady decrease of the wealth) with probability at least $p$. We present an exponential time algorithm which approximates this minimum initial wealth, and show that a polynomial time approximation is not possible unless P = NP. For the qualitative case, i.e. p=1, we show that the problem whether a given number is larger than or equal to the minimum initial wealth belongs to NP intersection coNP, and show that a polynomial time algorithm would yield a polynomial time algorithm for mean-payoff games, existence of which is a longstanding open problem. We also identify some classes of solvency MDPs for which this problem is in P. In all above cases the algorithms also give corresponding bankruptcy avoiding strategies.

Links

GPP202/12/P612, research and development project

Name: Formální verifikace stochastických systémů s reálným časem (Acronym: Formální verifikace stochastických systémů s reáln)

Investor: Czech Science Foundation

MUNI/A/0760/2012, interní kód MU

Name: Rozsáhlé výpočetní systémy: modely, aplikace a verifikace II. (Acronym: FI MAV II.)

Investor: Masaryk University, Category A

Citovat

BRÁZDIL, Tomáš, Taolue CHEN, Vojtěch FOREJT, Petr NOVOTNÝ and Aistis SIMAITIS. Solvency Markov Decision Processes with Interest. Online. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013). Dagstuhl, Germany: IBFI Schloss Dagstuhl, 2013, p. 487-499. ISBN 978-3-939897-64-4. Available from: https://dx.doi.org/10.4230/LIPIcs.FSTTCS.2013.487.

@inproceedings{1123332,
   author = {Brázdil, Tomáš and Chen, Taolue and Forejt, Vojtěch and Novotný, Petr and Simaitis, Aistis},
   address = {Dagstuhl, Germany},
   booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)},
   doi = {http://dx.doi.org/10.4230/LIPIcs.FSTTCS.2013.487},
   keywords = {stochastic systems; markov decision processes; reward functions},
   howpublished = {elektronická verze "online"},
   language = {eng},
   location = {Dagstuhl, Germany},
   isbn = {978-3-939897-64-4},
   pages = {487-499},
   publisher = {IBFI Schloss Dagstuhl},
   title = {Solvency Markov Decision Processes with Interest},
   url = {http://drops.dagstuhl.de/opus/volltexte/2013/4395/pdf/37.pdf},
   year = {2013}
}

TY  - JOUR
ID  - 1123332
AU  - Brázdil, Tomáš - Chen, Taolue - Forejt, Vojtěch - Novotný, Petr - Simaitis, Aistis
PY  - 2013
TI  - Solvency Markov Decision Processes with Interest
PB  - IBFI Schloss Dagstuhl
CY  - Dagstuhl, Germany
SN  - 9783939897644
KW  - stochastic systems
KW  - markov decision processes
KW  - reward functions
UR  - http://drops.dagstuhl.de/opus/volltexte/2013/4395/pdf/37.pdf
L2  - http://drops.dagstuhl.de/opus/volltexte/2013/4395/pdf/37.pdf
N2  - Solvency games, introduced by Berger et al., provide an abstract framework for modeling decisions of a risk-averse investor, whose goal is to avoid ever going broke. We study a new variant of this model, where in addition to stochastic environment and fixed increments and decrements to the investor's wealth we introduce interest, which is earned or paid on the current level of savings or debt, respectively. We concentrate on problems related to the minimum initial wealth sufficient to avoid bankrupting (i.e. steady decrease of the wealth) with probability at least $p$. We present an exponential time algorithm which approximates this minimum initial wealth, and show that a polynomial time approximation is not possible unless P = NP. For the qualitative case, i.e. p=1, we show that the problem whether a given number is larger than or equal to the minimum initial wealth belongs to NP intersection coNP, and show that a polynomial time algorithm would yield a polynomial time algorithm for mean-payoff games, existence of which is a longstanding open problem. We also identify some classes of solvency MDPs for which this problem is in P. In all above cases the algorithms also give corresponding bankruptcy avoiding strategies.
ER  -

BRÁZDIL, Tomáš, Taolue CHEN, Vojtěch FOREJT, Petr NOVOTNÝ and Aistis SIMAITIS. Solvency Markov Decision Processes with Interest. Online. In \textit{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)}. Dagstuhl, Germany: IBFI Schloss Dagstuhl, 2013, p.~487-499. ISBN~978-3-939897-64-4. Available from: https://dx.doi.org/10.4230/LIPIcs.FSTTCS.2013.487.

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