  A risk-neutral method is always used to price and hedge contingent claims in
complete market, but another method based on utility maximization or risk
minimization is wildly used in more general case. One can find all kinds of
special risk measure in literature. In this paper, instead of using market
modified risk measure, we use a kind of risk measure induced by
g_\Gamma-solution or the minimal solution of a Constrained Backward Stochastic
Differential Equation (CBSDE) directly when constraints on wealth and portfolio
process comes to our consideration. Such g_\Gamma-solution and the risk measure
generated by it is well defined on appropriate space under suitable conditions.
We adopt the inf-convolution of convex risk measures to solve some optimization
problem. A dynamic version risk measures defined through g_\Gamma-solution and
some similar results about optimal problem can be got in our new framework and
by our new approach.
