Fdtxjr

How strictly should I take "Candidates must be local"?

What was the Kree's motivation in Captain Marvel?

Is it possible to avoid unpacking when merging Association?

Reversed Sudoku

Conservation of Mass and Energy

Are babies of evil humanoid species inherently evil?

Was Luke Skywalker the leader of the Rebel forces on Hoth?

What does "the touch of the purple" mean?

Filtering SOQL results with optional conditionals

Difference on montgomery curve equation between EFD and RFC7748

UART pins to unpowered MCU?

Can one live in the U.S. and not use a credit card?

What's the "normal" opposite of flautando?

Latex does not go to next line

Bash script should only kill those instances of another script's that it has launched

Virginia employer terminated employee and wants signing bonus returned

Are there historical instances of the capital of a colonising country being temporarily or permanently shifted to one of its colonies?

Could you please stop shuffling the deck and play already?

When a wind turbine does not produce enough electricity how does the power company compensate for the loss?

Plausibility of Mushroom Buildings

In the quantum hamiltonian, why does kinetic energy turn into an operator while potential doesn't?

How many characters using PHB rules does it take to be able to have access to any PHB spell at the start of an adventuring day?

They call me Inspector Morse

Why does Captain Marvel assume the people on this planet know this?

Why is the ratio of two returns martingale?

Futures pricing and futures price process under the real world measureEvaluating Expectation of stochastic processGirsanov theorem for Ito diffusion processWhy is a discounted price process a local martingale under the Risk Neutral Measure?Girsanov theorem calculations helpHelp with change of measure and martingalesExpectation $ mathbb E^mathbb P^tau_tleft[ X_tau(T)Y_tauright] $ and measure change.How to solve this change in numerairestochastic representation using Girsanov's formulaWhat is the Radon-Nikodym density $dP^∗ /d P$ of the unique $P^ ∗ ∼ P$ such that the discounted price $S^*_t := S_t /B_t$ is a $P^∗$-martingale

1

$begingroup$

If we have a ratio of two fund returns, under the risk-neutral measure $y=frac left. F_T^2 middle/ F_0^2 right.left. F_T^1 middle/ F_0^1 right.$.
Let $X_t$ represents the price of asset 2 at time $t$.
$$Xt=E_tleft[fracF_T^2expleft(int_0^T r_u d_u right)right]$$
Then it can be seen that
$$X_t=fracF_t^2 expleft( int_0^t r_u d_u right ) underbrace E_tleft[ frac left. F_T^2 middle/ F_t^2 right. expleft(int_t^T r_u d_u right)right] _=1$$
My question: why is the last expectation equal to $1$?

probability-theory stochastic-processes stochastic-calculus conditional-probability stochastic-integrals

share|cite|improve this question

edited 2 days ago

Lee David Chung Lin

4,38031242

asked 2 days ago

veryBigmanveryBigman

153

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Please check if I messed up the math in my edit. BTW if you're doing this kind of big fractions a lot you should learn to use the middle slash, as well as a good habit of using the automatically sizing delimiters.
  $endgroup$
  – Lee David Chung Lin
  2 days ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thanks for your help. I appreciate it and will follow your advice in my future post
  $endgroup$
  – veryBigman
  yesterday
  

  
  
  
  

add a comment | 

1

$begingroup$

If we have a ratio of two fund returns, under the risk-neutral measure $y=frac left. F_T^2 middle/ F_0^2 right.left. F_T^1 middle/ F_0^1 right.$.
Let $X_t$ represents the price of asset 2 at time $t$.
$$Xt=E_tleft[fracF_T^2expleft(int_0^T r_u d_u right)right]$$
Then it can be seen that
$$X_t=fracF_t^2 expleft( int_0^t r_u d_u right ) underbrace E_tleft[ frac left. F_T^2 middle/ F_t^2 right. expleft(int_t^T r_u d_u right)right] _=1$$
My question: why is the last expectation equal to $1$?

probability-theory stochastic-processes stochastic-calculus conditional-probability stochastic-integrals

share|cite|improve this question

edited 2 days ago

Lee David Chung Lin

4,38031242

asked 2 days ago

veryBigmanveryBigman

153

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Please check if I messed up the math in my edit. BTW if you're doing this kind of big fractions a lot you should learn to use the middle slash, as well as a good habit of using the automatically sizing delimiters.
  $endgroup$
  – Lee David Chung Lin
  2 days ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thanks for your help. I appreciate it and will follow your advice in my future post
  $endgroup$
  – veryBigman
  yesterday
  

  
  
  
  

add a comment | 

$begingroup$

If we have a ratio of two fund returns, under the risk-neutral measure $y=frac left. F_T^2 middle/ F_0^2 right.left. F_T^1 middle/ F_0^1 right.$.
Let $X_t$ represents the price of asset 2 at time $t$.
$$Xt=E_tleft[fracF_T^2expleft(int_0^T r_u d_u right)right]$$
Then it can be seen that
$$X_t=fracF_t^2 expleft( int_0^t r_u d_u right ) underbrace E_tleft[ frac left. F_T^2 middle/ F_t^2 right. expleft(int_t^T r_u d_u right)right] _=1$$
My question: why is the last expectation equal to $1$?

probability-theory stochastic-processes stochastic-calculus conditional-probability stochastic-integrals

share|cite|improve this question

edited 2 days ago

Lee David Chung Lin

4,38031242

asked 2 days ago

veryBigmanveryBigman

153

$endgroup$

share|cite|improve this question

edited 2 days ago

Lee David Chung Lin

4,38031242

asked 2 days ago

veryBigmanveryBigman

153

share|cite|improve this question

edited 2 days ago

Lee David Chung Lin

4,38031242

asked 2 days ago

veryBigmanveryBigman

153

edited 2 days ago

Lee David Chung Lin

4,38031242

edited 2 days ago

Lee David Chung Lin

4,38031242

asked 2 days ago

veryBigmanveryBigman

153

asked 2 days ago

veryBigmanveryBigman

153