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# Portfolio

Let {S(t)}, t≥0 be an N-dimensional price process.

- A portfolio {h(t)}, t≥0 is an N-dim adapted process.
- The corresponding value process {V
^{h}(t)}, t≥0 is given by

V^{h}(t)=∑^{n}_{i=1}h^{i}(t)S^{i}(t) - A portfolio is self-financing if

V^{h}(t+Δ)- V^{h}(t)=∑^{n}_{i=1}h^{i}(t)(S^{i}(t+Δ)-S^{i}(t)) (discrete time)

dV^{h}(t)=∑^{n}_{i=1}h^{i}(t)dS^{i}(t) (continuous time)

Questions: Magnus Wiktorsson

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