# Financial mathematics

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- | Nonlocal equations are common in financial mathematics because the prices of assets can be modeled following any [[Levy process]]. In particular jump processes are natural since asset prices can have a sudden change. | + | Nonlocal equations are common in financial mathematics because the prices of assets can be modeled following any [[Levy processes|Levy process]]. In particular jump processes are natural since asset prices can have a sudden change. |

The Black–Scholes model, which is used to price derivatives, is essentially a parabolic integro-differential equation for European options, and an [[obstacle problem]] for American options. | The Black–Scholes model, which is used to price derivatives, is essentially a parabolic integro-differential equation for European options, and an [[obstacle problem]] for American options. |

## Revision as of 16:51, 23 January 2012

Nonlocal equations are common in financial mathematics because the prices of assets can be modeled following any Levy process. In particular jump processes are natural since asset prices can have a sudden change.

The Black–Scholes model, which is used to price derivatives, is essentially a parabolic integro-differential equation for European options, and an obstacle problem for American options.

A good reference for financial modeling with jump processes is the book of Rama Cont and Peter Tankov ^{[1]}

## Refences

- ↑ Cont, Rama; Tankov, Peter (2004),
*Financial modelling with jump processes*, Chapman & Hall/CRC Financial Mathematics Series, Chapman & Hall/CRC, Boca Raton, FL, ISBN 978-1-58488-413-2