Solution to exchanges 10.3 puzzle
Robin Ryder · ACM SIGecom Exchanges · 2012
First, a quick recap of the problem: the payout is a random variable X ; we assume we know its distribution F , and in particular that we know E F [ X ]. We are looking for a function ω (·,·) such that E F [ ω ( t , X )] = r · t , where r is the non-contingency hourly rate. Initially, we impose that ∀ t , ω ( t , 0) = 0 and that ω is linear in t .