Discounted wealth equation in discrete time
Relative to
a positive
numéraire,
a predictable self-financing
strategy with risky holdings
θt and discounted risky prices
Xt has discounted value
Vt=V0+∑s=1tθs⋅(Xs−Xs−1).
Thus its gains are the
discrete stochastic integral of its holdings against discounted price increments.
