Given That $d Y _ { t } = b d W _ { t }$

question 10

Multiple Choice

Given that $d Y _ { t } = b d W _ { t }$ and $X _ { t } = e ^ { Y t }$ , what is $d X _ { t }$ ?

• A) \(e ^ { b d W _ { t } }\)
• B) \(X _ { t } e ^ { b ^ { 2 } dt + Y _ { t } d W _ { t } }\)
• C) \(\ln \left( X _ { t } \right) \left[ \frac { 1 } { 2 } b ^ { 2 } d t + b d W _ { t } \right]\)
• D) \(b X _ { t } \left[ \frac { 1 } { 2 } b d t + d W _ { t } \right]\)

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Definitions:

Three-strikes

A legal principle mandating harsher sentences for repeat offenders, typically after three serious crimes.

Mandatory Minimum

A legal requirement that dictates the minimum sentence a judge must impose for a particular crime, reducing judicial discretion.

Rehabilitation

A process aimed at enabling individuals to restore their skills, health, or abilities, often used in the context of recovery from injury or in criminal justice.

Nothing Works

A controversial perspective in criminology that argues traditional rehabilitation programs are ineffective in reducing recidivism among convicted criminals.