Kenneth Ng
The Ohio State University
Title
Forward Performance Processes under Multiple Default Risks
Abstract
This article constructs a forward exponential utility when the underlying risky assets are exposed to default risk. In the first part, by employing the Jacod-Pham decomposition on the random field, we propose an ansatz based on a number of recursively defined, indexed infinite horizon BSDEs. The unique existence and the boundedness of solutions of the BSDEs are established. We then provide a rigorous verification of the required (super)martingale property of the ansatz, which confirms that the ansatz is indeed a forward exponential utility. In the second part, we consider a stochastic factor model and constructs a forward exponential utility using solutions of ergodic BSDEs as the limits of the infinite horizon BSDEs. We further provide the economic meaning of the solution component of the ergodic BSDE -- the risk-sensitive growth rate of the optimal wealth process.