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Finite-time optimal control of a process leaving an interval
Consider the optimal control problem of leaving an interval ( – a, a ) in a limited playing time. In the discrete-time problem, a is a positive integer and the player's position is given by a simple random walk on the integers with initial position x. At each time instant, the player chooses a...
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| Published in: | Journal of applied probability 1996-09, Vol.33 (3), p.714-728 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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| Online Access: | Get full text |
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| cites | cdi_FETCH-LOGICAL-c110t-8c6d276599344211ed2ae2b6840d0ef787bc9901d9d4bf7118c72801d927bb4c3 |
| container_end_page | 728 |
| container_issue | 3 |
| container_start_page | 714 |
| container_title | Journal of applied probability |
| container_volume | 33 |
| creator | Mcbeth, Douglas W. Weerasinghe, Ananda P. N. |
| description | Consider the optimal control problem of leaving an interval (
– a, a
) in a limited playing time. In the discrete-time problem,
a
is a positive integer and the player's position is given by a simple random walk on the integers with initial position
x.
At each time instant, the player chooses a coin from a control set where the probability of returning heads depends on the current position and the remaining amount of playing time, and the player is betting a unit value on the toss of the coin: heads returning +1 and tails − 1. We discuss the optimal strategy for this discrete-time game. In the continuous-time problem the player chooses infinitesimal mean and infinitesimal variance parameters from a control set which may depend upon the player's position. The problem is to find optimal mean and variance parameters that maximize the probability of leaving the interval [
— a, a
] within a finite time
T
> 0. |
| doi_str_mv | 10.1017/S0021900200100154 |
| format | article |
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– a, a
) in a limited playing time. In the discrete-time problem,
a
is a positive integer and the player's position is given by a simple random walk on the integers with initial position
x.
At each time instant, the player chooses a coin from a control set where the probability of returning heads depends on the current position and the remaining amount of playing time, and the player is betting a unit value on the toss of the coin: heads returning +1 and tails − 1. We discuss the optimal strategy for this discrete-time game. In the continuous-time problem the player chooses infinitesimal mean and infinitesimal variance parameters from a control set which may depend upon the player's position. The problem is to find optimal mean and variance parameters that maximize the probability of leaving the interval [
— a, a
] within a finite time
T
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– a, a
) in a limited playing time. In the discrete-time problem,
a
is a positive integer and the player's position is given by a simple random walk on the integers with initial position
x.
At each time instant, the player chooses a coin from a control set where the probability of returning heads depends on the current position and the remaining amount of playing time, and the player is betting a unit value on the toss of the coin: heads returning +1 and tails − 1. We discuss the optimal strategy for this discrete-time game. In the continuous-time problem the player chooses infinitesimal mean and infinitesimal variance parameters from a control set which may depend upon the player's position. The problem is to find optimal mean and variance parameters that maximize the probability of leaving the interval [
— a, a
] within a finite time
T
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– a, a
) in a limited playing time. In the discrete-time problem,
a
is a positive integer and the player's position is given by a simple random walk on the integers with initial position
x.
At each time instant, the player chooses a coin from a control set where the probability of returning heads depends on the current position and the remaining amount of playing time, and the player is betting a unit value on the toss of the coin: heads returning +1 and tails − 1. We discuss the optimal strategy for this discrete-time game. In the continuous-time problem the player chooses infinitesimal mean and infinitesimal variance parameters from a control set which may depend upon the player's position. The problem is to find optimal mean and variance parameters that maximize the probability of leaving the interval [
— a, a
] within a finite time
T
> 0.</abstract><doi>10.1017/S0021900200100154</doi><tpages>15</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0021-9002 |
| ispartof | Journal of applied probability, 1996-09, Vol.33 (3), p.714-728 |
| issn | 0021-9002 1475-6072 |
| language | eng |
| recordid | cdi_crossref_primary_10_1017_S0021900200100154 |
| source | JSTOR Archival Journals |
| title | Finite-time optimal control of a process leaving an interval |
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