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.
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