Asymptotic option price with bounded expected loss

Seongjoo Song, Jongwoo Song

Research output: Contribution to journalArticlepeer-review


This paper studies the problem of option pricing in an incomplete market, where the exact replication of an option may not be possible. In an incomplete market, we suppose a situation where a hedger wants to invest as little as possible at the beginning, but he/she wants to have the expected squared loss at the end not exceeding a certain constant. We study this problem when the log of the underlying asset price process is compound Poisson, which converges to a Brownian motion with drift. In the limit, we use the mean-variance approach to find a hedging strategy which minimizes the expected squared loss for a given initial investment. Then we find the asymptotic minimum investment with the expected squared loss bounded by a given upper bound. Some numerical results are also provided.

Original languageEnglish
Pages (from-to)323-334
Number of pages12
JournalJournal of the Korean Statistical Society
Issue number4
StatePublished - Dec 2008

Bibliographical note

Funding Information:
This research was supported by a Korea University Grant.


  • 60F05
  • 91B28
  • Bounded loss
  • Compound Poisson processes
  • Option pricing
  • Weak convergence
  • primary
  • secondary


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