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:

Joint Tenancy

A form of co-ownership where parties own property equally with the right of survivorship, meaning upon the death of one tenant, their share passes to the surviving tenant(s).

Tenancy

Tenancy is a legal term describing the possession and use of land or property rented from another, establishing rights and responsibilities between landlord and tenant.

Survival Clause

A contract provision that stipulates which parts of the agreement remain in effect after the contract has ended.

Wrongfully Abandons

Occurs when a party unlawfully leaves or forsakes their responsibility or property without justification.