Bounded solutions to backward SDE's with jumps for utility optimization and indifference hedging

By Dirk Becherer. 2006

207 citations recorded by the source corpus.

We prove results on bounded solutions to backward stochastic equations driven by random measures. Those bounded BSDE solutions are then applied to solve different stochastic optimization problems with exponential utility in models where the underlying filtration is noncontinuous. This includes results on portfolio optimization under an additional liability and on dynamic utility indifference valuation and partial hedging in incomplete financial markets which are exposed to risk from unpredictable events. In particular, we characterize the limiting behavior of the utility indifference hedging strategy and of the indifference value process for vanishing risk aversion.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/a0e51de902d11ac7f38fe833857311846ba8b585

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Citations in the corpus

A new existence result for quadratic BSDEs with jumps with application to the utility maximization problem (2010, methodology): “However and contrary to the papers [ BEC06 ] or [MOR08] already dealing with a discontinuous model, the originality of the present paper is that we study existence for a specific class of quadratic BSDEs with jumps without assuming the finiteness of the Levy measure.”
Discrete time approximation of decoupled Forward-Backward SDE with jumps (2008, background): “Such equations naturally appear in hedging problems, see e.g. Eyraud-Loisel [13], or in stochastic control, see e.g. Tang and Li [22] and the recent paper Becherer [3] for an application to exponential utility maximization in finance.”
Reflected and doubly reflected BSDEs with jumps: A priori estimates and comparison (2008, background): “1 Basic Problems With the exception of Becherer [3], previous works on BSDEs with jumps (see e.”
Minimal Entropy Martingale Measure (2010, background): “This topic has first been studied in [4], [58], [59], [64]; later work has examined intertemporally dynamic extensions ([5], [51]), descriptions via BSDEs in specific models ([6], [51]), extensions to more general payoff structures ([38], [47], [48], [61]), etc.”
Backward stochastic differential equations with time delayed generators - results and counterexamples (2010, background): “For instance, [10] discusses the existence of a solution in case the generator is of quadratic growth in the control variable; the existence of a solution for BSDE driven on a more general stochastic basis, created by Lévy processes, respectively, continuous martingales, is considered respectively i”