“Self-financing portfolio”的意思、由来-开放百科全书

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Self-financing portfolio

释义

Mathematical definition
Discrete time
See also
References

In financial mathematics, a self-financing portfolio is a portfolio having the feature that, if there is no exogenous infusion or withdrawal of money, the purchase of a new asset must be financed by the sale of an old one.

Mathematical definition

Let denote the number of shares of stock number 'i' in the portfolio at time , and the price of stock number 'i' in a frictionless market with trading in continuous time. Let

Then the portfolio is self-financing if

^[1]

Discrete time

Assume we are given a discrete filtered probability space , and let be the solvency cone (with or without transaction costs) at time t for the market. Denote by . Then a portfolio (in physical units, i.e. the number of each stock) is self-financing (with trading on a finite set of times only) if

for all we have that with the convention that .^[2]

If we are only concerned with the set that the portfolio can be at some future time then we can say that .

If there are transaction costs then only discrete trading should be considered, and in continuous time then the above calculations should be taken to the limit such that .

References

1. ^{{cite book|first=Tomas|last=Björk|title=Arbitrage theory in continuous time|edition=3rd|page=87|publisher=Oxford University Press|year=2009|isbn=978-0-19-877518-8}}
2. ^{{cite journal|last=Hamel|first=Andreas|last2=Heyde|first2=Frank|last3=Rudloff|first3=Birgit|date=November 30, 2010|title=Set-valued risk measures for conical market models|url=https://arxiv.org/PS_cache/arxiv/pdf/1011/1011.5986v1.pdf|accessdate=February 2, 2011|format=pdf}}

1 : Mathematical finance

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Mathematical definition

Discrete time

See also

References