I know that the need for a portfolio/strategy to be self-financing (the purchase of a new asset needs to be funded by selling of an older one/ones) is very helpful when attempting to price derivatives due being able to create replications of the derivative's payoffs, etc.

However, do we gain anything (such as a "wrong" but more useful/parsimonious model) from requiring this condition of a portfolio/strategy outside of valuation, specifically, when we're also not working under the risk-neutral measure? e.g. analyzing the profitability of a trading/investment strategy in practice.

Or does this assumption just move our model further away from how our portfolio/strategy would actually function due to market frictions (slippage, transaction fees, etc.) without providing a greater upside to model correctness/performance?

Thanks! :)

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    $\begingroup$ Not 100% sure what you're asking, but I think in general you can write Target payoff - Payoff self-financing strategy = P/L. So having a self-financing strategy is always useful as the above can be used to set E[P/L] = 0 or minimize Var [P/L] etc by tweaking your self-financing portfolio strategy. Risk-neutral or real-world doesn't matter since (no) arbitrage is conserved under any valid change of measure, hence the use of the term equivalent in 'equivalent martingale measure' which you often hear. $\endgroup$
    – Frido
    Commented Jun 8, 2023 at 10:07
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    $\begingroup$ Finance is different from Physics, but Self Financing Condition in Finance is similar and just as useful as Conservation of Energy in Physics. Except that it is conservation of money rather than energy. $\endgroup$
    – nbbo2
    Commented Jun 8, 2023 at 15:40
  • $\begingroup$ @Frido I think you pretty much addressed it and thank you for the information, I get why one would want to minimize Var[P/L], but when would one want to set E[P/L]? Is this for creating a self-financing strategy that replicates the payoff of the Target in expectation? (for valuation puroses, etc.) $\endgroup$
    – QMath
    Commented Jun 9, 2023 at 22:27
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    $\begingroup$ @QMath Yes for valuation / pricing, but then actually you'd want to have, and I should have written, P/L = 0. If exact replication / pricing is not possible then the next best thing is minimize the PL variance. $\endgroup$
    – Frido
    Commented Jun 10, 2023 at 7:09


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