mmas_sde_2006

mmas_sde_2006 - Essential questions for the exam 2006 1...

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Essential questions for the exam 2006 1. Formulate two models based on stochastic differential equations. Discuss the choise of noise, numerical method and Ito or Stratonovich form. 2. Formulate the basic properties a Wienerprocess. 3. De±ne the Ito integral by the limit of the forward Euler method and show that the limit is independent of the partition used in the time discretization. 4. Show by an example that piecewise linear approximation of the Wienerprocess in a SDE approximates Stratonovich integrals. 5. Show by Itos formula that if u solves Kolmogorov’s backward equation with data u ( T,x )= g ( x ), then u ( t, x )= E [ g ( X ( T )) | X ( t )= x ] , where X is the solution of a certain SDE ( which?). 6. Formulate and prove a theorem on error estimates for weak convergence of the forward Euler method for SDE’s. 7. Motivate the use of Monte-Carlo methods to compute Europian options based on a basket of several stocks and discuss some possibilities of methods of variance reduction. 8. State and derive Ito’s formula.
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This note was uploaded on 12/14/2011 for the course MAD 5932 taught by Professor Gallivan during the Fall '06 term at FSU.

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mmas_sde_2006 - Essential questions for the exam 2006 1...

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