MATHEMATICA BOHEMICA, Vol. 126, No. 2, pp. 275-280 (2001)

On Bellman systems without zero order term in the context of risk sensitive differential games

A. Bensoussan, J. Frehse

A. Bensoussan, CNES, 2, Place Maurice Quentin, 75039 Paris CEDEX 01, France; J. Frehse, Institut für Angewandte Mathematik, Universität Bonn, Beringstr. 6, 53115 Bonn, Germany, e-mail:

Abstract: 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.

Keywords: diagonal elliptic systems, quadratic growth, stochastic differential games, Bellman equation, risk sensitive control

Classification (MSC2000): 91A15, 93C20, 93E20, 91A80

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