Abstract
We discuss utility maximization problems with exponential preferences in an incomplete market where the risky asset dynamics is described by a pure jump process driven by two independent Poisson processes. This includes results on portfolio optimization under an additional European claim. Value processes of the optimal investment problems, optimal hedging strategies and the indifference price are represented in terms of solutions to backward stochastic equations driven by the Poisson martingales. Via a duality result, the solution to the dual problems is derived. In particular, an explicit expression for the density of the minimal martingale measure is provided. The Markovian case is also discussed. This includes either asset dynamics dependent on a pure jump stochastic factor or claims written on a correlated non tradable asset.
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Ceci, C., Gerardi, A. Utility indifference valuation for jump risky assets. Decisions Econ Finan 34, 85–120 (2011). https://doi.org/10.1007/s10203-010-0107-6
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DOI: https://doi.org/10.1007/s10203-010-0107-6
Keywords
- Utility maximization
- Backward stochastic differential equations
- Jump processes
- Dynamic indifference valuation
- Minimal entropy measure