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2841概率中等derivationmedium

Signed Compound Poisson Order Flow

题目

Market buys arrive as +1+1 and sells as 1-1. The number of trades in a minute is NPoisson(λ)N\sim\mathrm{Poisson}(\lambda), and conditional on a trade, the sign is +1+1 with probability pp and 1-1 with probability 1p1-p, independently. Let SS be the net signed flow in that minute. Find the MGF of SS, and compute E[S]E[S] and Var(S)\mathrm{Var}(S).

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E[S]

Var(S)