We have $dB_t = rB_tdt$.

We are told that this corresponds to a "bank"..... how? When I insert money into a bank, how does this correspond to buying an asset for the price $B_t$?

It would make more sense to say it is a bond, yet my book insists this is a "bank".


Well, I do not think there is a large difference: Given you deposit money at a Bank the value of this deposit changes according to $$\frac{dB_t}{B_t} = r dt$$ which simply means there is no uncertainty with respect to this evolution (instead of incorporating a risky component $dW_t$. If you really want to interpret the risk-less asset as a bond you are probably faced to some issues (the bond should not exhibit a maturity but instead should only pay interest). Therefore I would agree that it is best to interpret the risk-less term as a bank deposit.

  • 2
    $\begingroup$ Yes, for the Bond interpretation you would have to consider a strategy of constantly rolling over whichever bond(s)/bill(s) in a bond portfolio expire today, which gets messy to explain. $\endgroup$ – noob2 Feb 8 '17 at 20:33

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.