Some Problems Related to the Black-Scholes Type Security Markets

Jiongmin Yong
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Jiongmin Yong: Department of Mathematics and Institute of Mathematical Finance, Fudan University, Shanghai 200433, China

Chapter 18 in Stochastic Processes and Applications to Mathematical Finance, 2004, pp 369-400 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractIn Black-Scholes type security markets, the completeness, arbitrage-free condition, pricing (European) contingent claims, etc. are thought to be well-understood by now. However, some careful studies show that the issue seems not to be as simple as expected. Problems related to the above-mentioned notions lead to several interesting questions for Itô's integrals and (backward) stochastic differential equations. In this paper, some relevant partial results will be presented and several open questions will be posed.

Keywords: Stochastic Processes; Stochastic Differential Equations; Malliavin Calculus; Stochastic Control and Optimization; Functionals of Brownian Motions and Lévy Processes; Stochastic Models of Financial Market; Derivative Pricing; Hedging Problem (search for similar items in EconPapers)
Date: 2004
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