Continuous Stochastic Calculus with Applications to Finance by Michael Meyer
The prolonged boom in the US and European stock markets has led to increased interest in the mathematics of security markets, most notably in the theory of stochastic integration. This text gives a rigorous development of the theory of stochastic integration as it applies to the valuation of derivative securities. It includes all the tools necessary for readers to understand how the stochastic integral is constructed with respect to a general continuous martingale.
The author develops the stochastic calculus from first principles, but at a relaxed pace that includes proofs that are detailed, but streamlined to applications to finance. The treatment requires minimal prerequisites-a basic knowledge of measure theoretic probability and Hilbert space theory-and devotes an entire chapter to application in finances, including the Black Scholes market, pricing contingent claims, the general market model, pricing of random payoffs, and interest rate derivatives.
Continuous Stochastic Calculus with Application to Finance is your first opportunity to explore stochastic integration at a reasonable and practical mathematical level. It offers a treatment well balanced between aesthetic appeal, degree of generality, depth, and ease of reading.