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This looks like a classic real options problem. Essentially, each decision is an option which will be chosen strategically: the owner will chose a vector of actions from all possible actions, $A\in\mathcal{A}$, that maximizes expected utility given the distributions of key variables and outcomes. If the owner is well-capitalized, maximizing the expected ...


Adding to the list of products mentioned in the comments: zero-coupon bond options have analytic solutions too (in terms of noncentral chi-squared distribution function), and caps and floors, when seen as portfolios of zero-coupon bond options (see Brigo and Mercurio book).


DataFrame df with a few random returns that I made up: import pandas as pd df = pd.DataFrame({'rets': (.5, .5, .4, .3)}) Add cum_rets column: df['cum_rets'] = (1 + df['rets']).cumprod() - 1 Add inv_cum_rets colum: df['inv_cum_rets'] = ((1 + df['cum_rets']) / (1 + df['rets'])) - 1 If you want it lined up with your original returns, just shift it up 1 row ...


Maybe a "statistical mechanics" approach - paper at and code at From the paper abstract: "This consists of a statistical mechanical approach - analogous to the configuration model for networked systems - for ...

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