Search results
Results from the WOW.Com Content Network
His textbook Stochastic Calculus for Finance is used by numerous graduate programs in quantitative finance. [3] [4] The book was voted "Best New Book in Quantitative Finance" in 2004 by members of Wilmott website, and has been highly praised by scholars in the field. [5] Shreve is a Fellow of the Institute of Mathematical Statistics. [6]
An important application of stochastic calculus is in mathematical finance, in which asset prices are often assumed to follow stochastic differential equations.For example, the Black–Scholes model prices options as if they follow a geometric Brownian motion, illustrating the opportunities and risks from applying stochastic calculus.
Girsanov's theorem is important in the general theory of stochastic processes since it enables the key result that if Q is a measure that is absolutely continuous with respect to P then every P-semimartingale is a Q-semimartingale.
The calculus has been applied to stochastic partial differential equations as well. The calculus allows integration by parts with random variables; this operation is used in mathematical finance to compute the sensitivities of financial derivatives. The calculus has applications in, for example, stochastic filtering.
In mathematics, Itô's lemma or Itô's formula is an identity used in Itô calculus to find the differential of a time-dependent function of a stochastic process.It serves as the stochastic calculus counterpart of the chain rule.
Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling in the financial field. In general, there exist two separate branches of finance that require advanced quantitative techniques: derivatives pricing on the one hand, and risk and portfolio ...
As with ordinary calculus, integration by parts is an important result in stochastic calculus. The integration by parts formula for the Itô integral differs from the standard result due to the inclusion of a quadratic covariation term. This term comes from the fact that Itô calculus deals with processes with non-zero quadratic variation ...
In finance, the Vasicek model is a mathematical model describing the evolution of interest rates. It is a type of one-factor short-rate model as it describes interest rate movements as driven by only one source of market risk. The model can be used in the valuation of interest rate derivatives, and has also been adapted for credit markets.