The following stochastic differential equation describes the behaviour of the price St, t0, of a share. dSt = (a+bsin(t)) Stdt + σS₁dWt, where a, b, σ are constants such that a > 0, |b| < a, and σ > 0. (a) Compute the differential of the function F(t) defined by F(t) = ln(St). (b) Solve the equation for St with the initial value S(0) = So. (c) Compute E(In(St)) and Var(ln(St)) and state the distribution of In(St).

The following stochastic differential equation describes the behaviour of the price St, t0, of a share. dSt = (a+bsin(t)) Stdt + σS₁dWt, where a, b, σ are constants such that a > 0, |b| < a, and σ > 0. (a) Compute the differential of the function F(t) defined by F(t) = ln(St). (b) Solve the equation for St with the initial value S(0) = So. (c) Compute E(In(St)) and Var(ln(St)) and state the distribution of In(St).

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.

Chapter11: Differential Equations

Section11.1: Solutions Of Elementary And Separable Differential Equations

Problem 54E: Plant Growth Researchers have found that the probability P that a plant will grow to radius R can be...

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