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 <I>d</I>-dimensional Brownian motion W = (W₁,...;W_d)'</I> as well as an integer-valued random measure <I>μ(du, dy)</I>. 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) <I>C_t</I> of the 𝔽-investors with respect to the 𝔾-investors and describe the dynamics of <I>C_t</I> by two BSDEs. In the end, we give an example in which we can give the explicit expression of <I>C_t</I>. For the generalized Cox model we typically have that <I>C_t</I> ≥ 1 in contrast to the standard Cox model