Fully-Dynamic Risk-Indifference Pricing and No-Good-Deal Bounds

The seller's risk-indifference price evaluation is studied. We propose a dynamic risk-indifference pricing criterion derived from fully-dynamic risk measures on the L-p-spaces for p is an element of [1; infinity]. The concept of fully-dynamic risk measures extends the one of dynamic risk measures by adding the actual possibility of changing the risk perspectives over time. This family is then characterized by a double time index. Our framework fits well the study of both short- and long-term investments. In this paper we analyze whether the risk-indifference pricing criterion actually provides a proper convex price system. It turns out that, depending on p, this is not always the case. Then an extension of the framework beyond L-p becomes necessary. Furthermore, we consider the relationship of the fully-dynamic risk-indifference price with no-good-deal bounds. We shall provide necessary and sufficient conditions on the fully-dynamic risk measures so that the corresponding risk-indifference prices satisfy the no-good-deal bounds. Remarkably, the use of no-good-deal bounds also provides a method to select the risk measures and thus construct a proper fully-dynamic risk-indifference price system within the L-2-spaces.