Abstract
Stochastic analysis is a key tool in the recent study of Mathematical Finance. Stochastic analytical models in Mathematical Finance are classified into two types. One is a discrete model, in which the trading time is restricted to the set of natural numbers, and moreover the underlying probability space is often a finite set. The other is a continuous model, which admits the trading time to be any non-negative real number. In a lot of continuous models, stochastic differential equations govern the time evolution of the models. A short survey on these two models will be given.KeywordsEquivalent martingale measurePricing formulaCRR modelTrinomial modelStochastic integralBlack-Scholes modelImplied volatilityStochastic volatility modelSingle-factor model
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