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Let F a mutual fund with two assets A and B. Initially, F contains 1 unit of A, 1 unit of B, and there is 1 share allocated to Alice. At a later time, Bob deposits 2 units of A into F. How can I calculate the amount of shares to create and allocate to Bob?

I can convert all the assets into a pivot like USD, then create shares proprotionnally to the amount deposited. However this approach requires to have access to a ticker (in this case A/USD and B/USD). Is it possible to calculate the amount of shares without relying on a pivot?

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    $\begingroup$ You need to know the value of all assets A and B at the time Bob makes his investment, in USD or other numeraire. Can't do without that. It will determine the percentages of the fund that Alice and Bob own. $\endgroup$
    – nbbo2
    Jan 3 at 10:25

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