Geodesic
The Hamilton-Jacobi-Bellman equation for a class of differential games with random duration
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 1 (2009) no. 2, pp. 98-118

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The class of differential games with random duration is studied. It turns out that the problem with random duration of the game can be simplified to the standard problem with infinite time horizon. The Hamilton-Jacobi-Bellman equation which help us to find the optimal solution under condition of random duration of the processes is derived. The results are illustrated with a game-theoretical model of non-renewable resource extraction. The problem is analyzed under condition of Weibull distribution for the random terminal time of the game.
Keywords: differential games, Hamilton-Jacobi-Bellman equation, random duration, non-renewable resource extraction. 
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     author = {Ekaterina Shevkoplyas},
     title = {The {Hamilton-Jacobi-Bellman} equation for a class of differential games with random duration},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {98--118},
     publisher = {mathdoc},
     volume = {1},
     number = {2},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2009_1_2_a5/}
}
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Ekaterina Shevkoplyas. The Hamilton-Jacobi-Bellman equation for a class of differential games with random duration. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 1 (2009) no. 2, pp. 98-118. http://geodesic.mathdoc.fr/item/MGTA_2009_1_2_a5/