Sankhya: The Indian Journal of Statistics
1995, Volume 57, Series A, Pt. 1, pp. 161--165
STOCHASTIC DIFFERENCIAL GAMES : THE LINEAR QUADRATIC ZERO SUM CASE
R. ARDANUY, Universidad de Salamanca
SUMMARY. The paper considers the problem of finding optimal strategies, with two players, based on linear stochastic differential system d\xi = (A\xi + B_1 u^1 + B_2 u^2)dt +\sigma dW$. Using a minimax principle we found that the feedback optimal strategies are linear in the state of the system and may be calculated by solving a Ricatti matrix differential equation. We also formulate a separation principle that relates the solution in the deterministic case with the solution in the stochastic case, as in a linear stochastic control problem.
AMS (1985) subject classification. 93E05, 90D05, 90D25.
Key words and phrases. Stochastic differential games, stochastic optimization, separation principle.
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