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# Self financing portfolio

A self-financing portfolio is characterised by that all trades are financed by selling or buying assets in the portfolio. No money is withdrawn or inserted after the intial forming of the portfolio.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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