Bounded solutions to backward SDEs with jumps for utility optimization and indifference hedging

Dirk Becherer

193 citations0/0 files storedThe Annals of Applied Probability

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Stochastic processes and financial applications Economic theories and models Risk and Portfolio Optimization

Abstract

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.

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References

2003Limit Theorems for Stochastic Processes 1997Backward Stochastic Differential Equations in Finance 2000Backward stochastic differential equations and partial differential equations with quadratic growth 1997Backward stochastic differential equations and integral-partial differential equations 1994Necessary Conditions for Optimal Control of Stochastic Systems with Random Jumps 2010A Guided Tour through Quadratic Hedging Approaches 2000Pricing Via Utility Maximization and Entropy 2005Utility maximization in incomplete markets

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2008Quadratic BSDEs driven by a continuous martingale and applications to the utility maximization problem 2007Discrete-time approximation of decoupled Forward–Backward SDE with jumps 2008Reflected and doubly reflected BSDEs with jumps: A priori estimates and comparison 2015BSDEs with monotone generator driven by Brownian and Poisson noises in a general filtration 2010Backward stochastic differential equations with time delayed generators—results and counterexamples

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