Abstract
This paper considers the asset price movements in a financial market with a risky asset and a bond. The dynamics of the risky asset, modeled by a marked point process, depend on a stochastic factor, modeled also by a marked point process. The possibility of common jump times with the price is allowed. The problem studied is to determine a strategy maximizing the expected value of a utility function of the hedging error. Two different approaches are considered: an Hamilton Jacobi Bellmann equation is studied for a simplified model and a contraction technique is introduced for a more general model.
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Gerardi, A., Tardelli, P. Stochastic Control Methods: Hedging in a Market Described by Pure Jump Processes. Acta Appl Math 111, 233–255 (2010). https://doi.org/10.1007/s10440-009-9543-0
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DOI: https://doi.org/10.1007/s10440-009-9543-0