Dynamic CRRA-Utility Indifference Value in Generalized Cox Model

We assume that there exist two kinds of investors in the market, the 𝔽-investors and the 𝔾-investors. The 𝔽-investors have the market information 𝔽, which is given by a d-dimensional Brownian motion W = (W1,...;Wd)' as well as an integer-valued random measure μ(du, dy). The market might default at time ˜τ, modeled by the so called the generalized Cox model, and the information of the 𝔾-investors is the by the default, progressively enlarged fitration of 𝔽. We give the explicit form of the survival process. Then we derive the dynamic CRRA-utility indifference value(UIV) Ct of the 𝔽-investors with respect to the 𝔾-investors and describe the dynamics of Ct by two BSDEs. In the end, we give an example in which we can give the explicit expression of Ct. For the generalized Cox model we typically have that Ct ≥ 1 in contrast to the standard Cox model.