The evolution of the bank account is governed by which can be understood as geometric Brownian motion

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The evolution of the bank account is governed by

which can be understood as geometric Brownian motion with ? = 0. Manipulate the resulting Black?Scholes-equation to show that it is equivalent to the so-called transport equation

with the substitution V(B, t) = e^?r(T?t)U(B, t) and x = log B.

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A First Course in Quantitative Finance

ISBN: 978-1108419574

1st edition

Authors: Thomas Mazzoni

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Question Posted: Feb 19, 2020 09:27 AM

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The evolution of the bank account is governed by which can be understood as geometric Brownian motion

Question:

dB(t) = r B(t)dt дU дU +r- = 0. де дх

Step by Step Answer:

We start by using Itos lemma on the function VB t erTtUB t to obtain dV rTtVdt erTtdU Now ...View the full answer

A First Course in Quantitative Finance

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