한국전산응용수학회:학술대회논문집 (Proceedings of the Korean Society of Computational and Applied Mathematics Conference)
- 한국전산응용수학회 2003년도 KSCAM 학술발표회 프로그램 및 초록집
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- Pages.10-10
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- 2003
The mathematical backups in the option pricing theory
초록
Option pricing theory developed by Black and Sholes depends on an arbitrage opportunity argument. An investor can exactly replicate the returns to any option on that stock by continuously adjusting a portfolio consisting of a stock and a riskless bond. The value of the option equal the value of the replicating portfolio. However, transactions costs invalidate the Black-Sholes arbitrage argument for option pricing, since continuous revision implies infinite trading, Discrete revision using Black-Sholes deltas generates errors which are correlated with the market, and do not approach zero with more frequent revision when transactions costs are included. Stochastic calculus serves as a fundamental tool in the mathematical finance. We closely look at the utility maximization theory which is one of the main option valuation methods. We also see that how the stochastic optimal control problems and their solution methods are applied to the theory.
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