If $S$ is a martingale, then alle processes $((HS)_t)_t$ are martingales

Asked Jan 20 '23 at 22:32

Active Jan 20 '23 at 22:32

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I have just started with financial mathematics in discrete times, and while reading about martingales I came across this statement without proof, which I am not sure how I would prove. I would appreciate any help!

Statement: If $S$ is a martingale, then all processes $((HS)_t)_t$ are martingales, in particular $E[(HS)_T]=0$

asked Jan 20 '23 at 22:32

variableXYZ

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What is $H$ here? – user6247850 Jan 20 '23 at 22:59
@user6247850 a strategy, $(HS)_t$ would be a stochastic integral – variableXYZ Jan 20 '23 at 23:04

If $S$ is a martingale, then alle processes $((HS)_t)_t$ are martingales

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