Questions on Self-Financing, Gain Processes, and Collateral Discounting

Summary

The document raises technical questions about the self-financing condition in papers on funding, collateral, and discounting. It asks whether a displayed inequality involving changes in positions and asset prices contains an inconsistent superscript on the position variables. The issue concerns how portfolio value changes should be written when holdings and prices may be indexed by a party or account.

It also asks how to interpret a claim’s gain process alongside its value process, given that gain processes are familiar for assets through prices and cumulative dividends. The author questions whether the claim’s gain process is needed in the paper’s argument, since an apparent equality between the claim and portfolio gain processes does not seem to be used. The document supplies no answers, derivation, or resolution of either point. It is useful chiefly as a prompt to examine notation and the distinction between value and cumulative gains in funding models; its claims should not be treated as established conclusions.

Key ideas

• The self-financing equation is questioned for a potentially inconsistent position superscript.
• The document asks how claim value processes differ from claim gain processes.
• It raises whether equality of claim and portfolio gains is necessary to the argument.
• No answer or derivation is provided, so both issues remain unresolved.

Tags

# Self-financing condition and funding, collateral and discounting


# Self-financing condition and funding, collateral and discounting












I'm reading "Illustrating a problem in the self-financing condition in two 2010-2011 papers on funding, collateral and discounting" paper.

- Is it just me or authors have a typo in their main warning (***): $\theta$'s seem to have the superscript $A$ on one side, but not the other?

$$d\left(\sum_{i=1}^n \theta_i^A P_i^A \right) \not= \sum_{i=1}^n \theta_i dP_i^A $$

- The claim $Y$ has a value process, $V^Y$, but also a gain process (!?) $G^Y$. What is it (I understand gain processes for assets, price and cumulative dividend, does the concept extend to claims too?) and is it needed to complete the paper's arguments, as equality $G^Y=G^\Pi$ doesn't seem to be used anywhere?

Thank you for taking your time to look into my questions.

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