# Article

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Keywords:
diagonal elliptic systems; quadratic growth; stochastic differential games; Bellman equation; risk sensitive control
Summary:
Bellman systems corresponding to stochastic differential games arising from a cost functional which models risk aspects are considered. Here it leads to diagonal elliptic systems without zero order term so that no simple $L^{\infty }$-estimate is available.
References:
[1] A. Bensoussan, J. Frehse: Nonlinear elliptic systems in stochastic game theory. J. Reine Angew. Math. Mathematik 350 (1984), 23–67. MR 0743532
[2] H. Nagaï: Bellman equation of risk sensitive control. SIAM J. Control Optim. 34 (1996), 74–101. DOI 10.1137/S0363012993255302 | MR 1372906

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