A mathematical model for European/American options with uncertainty is presented. The uncertainty is represented by both randomness and fuzziness. The randomness and fuzziness are evaluated respectively by probabilistic expectation and fuzzy expectation defined by a possibility measure from the viewpoint of decision-maker’s subjective judgment. Prices of European call/put options with uncertainty are presented, and their valuation and properties are discussed under a reasonable assumption. The hedging strategies are also considered for marketability of the European options in portfolio selection. Further, the American options model with uncertainty is discussed by a numerical approach and is compared with the analytical case of the infinite terminal time. The buyer’s/seller’s rational range of the optimal expected price in each option is presented and the meaning and properties of the optimal expected prices are discussed.
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- Option Pricing Theory in Financial Engineering from the Viewpoint of Fuzzy Logic
- Springer Berlin Heidelberg
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