Geodesic
A time-dependent best choice problem with costs and random lifetime in organ transplants
Anna Krasnosielska1
1 Faculty of Mathematics and Information Science Warsaw University of Technology Pl. Politechniki 1 00-661 Warsaw, Poland
Applicationes Mathematicae, Tome 37 (2010) no. 3, pp. 257-274.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

This paper develops and analyzes a time-dependent optimal stopping problem and its application to the decision making process concerning organ transplants. Offers (organs for transplant) appear at jump times of a Poisson process. The values of the offers are i.i.d. random variables with a known distribution function. These values express the degree of histocompatibility between the donor and the recipient. The sequence of offers is independent of the jump times of the Poisson process. The decision about acceptance or rejection must be made at the time of appearance of the offer. When the offer is accepted, the decision process terminates and a reward is gained. The reward depends on the value of the selected offer, a discount function and a cost function related to aversion to risk. Otherwise, the decision process is continued until a random time $T$. After this time the reward is equal to zero. The aim of the decision maker is to maximize the expected mean reward. A first-order differential equation for the optimal mean reward is obtained.
DOI : 10.4064/am37-3-1
Keywords: paper develops analyzes time dependent optimal stopping problem its application decision making process concerning organ transplants offers organs transplant appear jump times poisson process values offers random variables known distribution function these values express degree histocompatibility between donor recipient sequence offers independent jump times poisson process decision about acceptance rejection made time appearance offer offer accepted decision process terminates reward gained reward depends value selected offer discount function cost function related aversion risk otherwise decision process continued until random time after time reward equal zero the decision maker maximize expected mean reward first order differential equation optimal mean reward obtained

Anna Krasnosielska 1

1 Faculty of Mathematics and Information Science Warsaw University of Technology Pl. Politechniki 1 00-661 Warsaw, Poland 
@article{10_4064_am37_3_1,
     author = {Anna Krasnosielska},
     title = {A time-dependent best choice problem with costs and random lifetime in organ transplants},
     journal = {Applicationes Mathematicae},
     pages = {257--274},
     publisher = {mathdoc},
     volume = {37},
     number = {3},
     year = {2010},
     doi = {10.4064/am37-3-1},
     zbl = {1206.92011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/am37-3-1/}
}
TY  - JOUR
AU  - Anna Krasnosielska
TI  - A time-dependent best choice problem with costs and random lifetime in organ transplants
JO  - Applicationes Mathematicae
PY  - 2010
SP  - 257
EP  - 274
VL  - 37
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/am37-3-1/
DO  - 10.4064/am37-3-1
LA  - en
ID  - 10_4064_am37_3_1
ER  - 
%0 Journal Article
%A Anna Krasnosielska
%T A time-dependent best choice problem with costs and random lifetime in organ transplants
%J Applicationes Mathematicae
%D 2010
%P 257-274
%V 37
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/am37-3-1/
%R 10.4064/am37-3-1
%G en
%F 10_4064_am37_3_1
Anna Krasnosielska. A time-dependent best choice problem with costs and random lifetime in organ transplants. Applicationes Mathematicae, Tome 37 (2010) no. 3, pp. 257-274. doi : 10.4064/am37-3-1. http://geodesic.mathdoc.fr/articles/10.4064/am37-3-1/

Cité par Sources :