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MMLU-Pro / 271 / Consider an arbitrage-free securities market model, in which the risk-free…

Problem

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question

Consider an arbitrage-free securities market model, in which the risk-free interest rate is constant. There are two nondividend-paying stocks whose price processes are:

S_1(t)=S_1(0)e^{0.1t+0.2Z(t)}

S_2(t)=S_2(0)e^{0.125t+0.3Z(t)}

where

Z(t)

is a standard Brownian motion ant

t\ge0

. What is the continuously compounded risk-free interest rate?

Plain-text mathematical notation (without MathML)

Consider an arbitrage-free securities market model, in which the risk-free interest rate is constant. There are two nondividend-paying stocks whose price processes are:
S₁(t)=S₁(0)e^(0.1t+0.2Z(t))
S₂(t)=S₂(0)e^(0.125t+0.3Z(t))
where Z(t) is a standard Brownian motion ant t≥0. What is the continuously compounded risk-free interest rate?

Original LaTeX notation

Consider an arbitrage-free securities market model, in which the risk-free interest rate is constant. There are two nondividend-paying stocks whose price processes are:
$S_1(t)=S_1(0)e^{0.1t+0.2Z(t)}$
$S_2(t)=S_2(0)e^{0.125t+0.3Z(t)}$
where $Z(t)$ is a standard Brownian motion ant $t\ge0$. What is the continuously compounded risk-free interest rate?

src

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Source and history

upstream_id / Original problem ID: 271
task_id: 16df9296-d0a4-570f-8f6f-000c003e7b40
task_key: default--test--271
task_revision_id: 1
config / split: default / test

Official source

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