Exponential utility maximization and indifference valuation with unbounded payoffs

Abstract

We solve an exponential utility maximization problem with unbounded payoffs under general portfolio constraints, via the theory of quadratic backward stochastic differential equations with unbounded terminal data. This generalizes the previous work of Hu et al. (2005) [Ann. Appl. Probab., 15, 1691-1712 from the bounded to an unbounded framework. Furthermore, we study utility indifference valuation of financial derivatives with unbounded payoffs, and derive a novel convex dual representation of the prices. In particular, we obtain new asymptotic behavior as the risk aversion parameter tends to either zero or infinity.

Consumption Investment Optimization with Epstein-Zin Utility in Incomplete Markets

“…Compared with Lemma B.2 in Xing (2017), our proof is more straightforward, which only depends on the exponential integrability of Y and relative entropy method. Hu et al (2018) solve an exponential utility maximization problem with unbounded payoffs using the similar technique.…”

Systems of ergodic BSDEs arising in regime switching forward performance processes

“…The case with unbounded terminal data is more challenging and was solved in [8] [9] [17], with [18] and [19] further showing the uniqueness of the solution. Their applications can be found in [1] and [24]. Recently, there have been a renewed interest in the corresponding quadratic BSDE systems due to their various applications in equilibrium problems, price impact models and nonzero sum games (see, for example, [10] [27] [28] [31] [32] and [42] with more references therein).…”