Assume an asset price S_t follows the geometric Brownian motion, dS_t = µS_tdt + σS_dW_t, where µ and σ are constants and r is the risk-free rate. 1. Using the Ito’s Lemma find the stochastic differential equation satisfied by the process Xt = S_t^n , where n is a constant. 2. Compute E[X_t] and Var[X_t]. 3. Using the Ito’s Lemma find the stochastic differential equation satisfied by the process Y_t = S_tert

Assume an asset price S_t follows the geometric Brownian motion, dS_t = µS_tdt + σS_dW_t, where µ and σ are constants and r is the risk-free rate. 1. Using the Ito’s Lemma find the stochastic differential equation satisfied by the process Xt = S_t^n , where n is a constant. 2. Compute E[X_t] and Var[X_t]. 3. Using the Ito’s Lemma find the stochastic differential equation satisfied by the process Y_t = S_tert

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter14: Discrete Dynamical Systems

Section14.3: Determining Stability

Problem 18E

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