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Variational Equality and Portfolio Optimization for Price Processes with Jumps

In: Stochastic Processes And Applications To Mathematical Finance

Author

Listed:
  • Hiroshi Kunita

    (Department of Mathematical Science, Nanzan University, Seirei-cho, Seto, 489-0863, Japan)

Abstract

We study the optimization of the portfolio/consumption which maximizes the expected value of utilities in the case where the price process has jumps, i.e., the solution of a SDE driven by a Lévy process. A duality method is taken. There are infinitely many equivalent martingale measures (or state price densities). Among them we find an optimal state price density, with respect to which the optimal contingent claim is attainable. For the proof, a useful variational equality is introduced.

Suggested Citation

  • Hiroshi Kunita, 2004. "Variational Equality and Portfolio Optimization for Price Processes with Jumps," World Scientific Book Chapters, in: Jiro Akahori & Shigeyoshi Ogawa & Shinzo Watanabe (ed.), Stochastic Processes And Applications To Mathematical Finance, chapter 9, pages 167-194, World Scientific Publishing Co. Pte. Ltd..
  • Handle: RePEc:wsi:wschap:9789812702852_0009
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