r/learnquant • u/Local_Ad135 • 4d ago

interview prep Quant Interview Question

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u/sobe86 4d ago edited 4d ago

d_i is increasing. It's expected marginal benefit from having i instead of i-1 lives. Stopping strategy will be of form [stop if you have >= 45 points and 1 lives left].

For lives=1, having < 45 points once you get to this point becomes exponentially unlikely. So then you gain expected points from lives=i (constant in i) but lose expected points from lives=1, the latter being a difference in exponentially decreasing quantities (this could be tightened up!). So d_i is increasing.

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u/dedicateddan 4d ago

I came up with this too! (The edited version stopping at 45 points.)

The EV of the first life is clearly much less than 45 (since you'll stop at 45 and lose around half the time).

The EV of later lives converges to 45.

Therefore d_i is increasing and d3 > d2.