The exp-UIV for Markets with Partial Information and Complete Information

Abstract

We consider an incomplete market with two information structures, complete and partial information and , respectively. The dynamics of the market are given by a risky asset driven by a m-dimensional Brownian motion W = (W₁, …, W_m)′ as well as an integer-valued random measure μ(du, dy). To study the values with respect to the different information filtrations, we introduce the concept of dynamic < ![CDATA[exp]] >-utility indifference value (UIV) of with respect to denoted by C_t and the concept of dynamic < ![CDATA[exp]] >-UIV of the contingent claim H denoted by C_t(H), and we describe the dynamics of C_t and C_t(H) by BSDEs.

Keywords:

• Jump markets w.r.t. different filtrations
• Dynamic exp-UIV
• BSDE techniques
• Enlargement of filtration

Mathematics Subject Classification (2000):

• 90A09
• 60H30
• 60G44

Additional information

Funding

This work is supported by National Natural Science Foundation of China under Grant No. 11171215 and Natural Science Foundation of Shanghai No. 13ZR142200.