Interview Question: Integration

Sample Question #193 (mathematics)

Find the closed-form solution to the following:

Integral 

where W(s) is a standard Brownian motion.

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5 Responses to Interview Question: Integration

  1. heath says:

    Why cant it be (W(t)^2)/2 or t^2 / 2 for limits of integral in terms of W(s) going from 0 to t or s going from to 0 to t.Is this not treated as a normal integral?

  2. Brett says:

    This is a real interview question. I don’t have the answer yet. (Stochastic calculus is my weakest area — I tell you guys this because too many readers and visitors have asked me if a quant needs to know everything. The answer is no. Even real smart quants like Robert Merton don’t know everything! 🙂  )
     
    -brett

  3. Brett says:

    I can’t quite get the final result, but Vincent’s answer seems to be right.
     

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