Defining the payback period for nonconventional cash flows: an axiomatic approach

Battle Count: 71

The paper is primarily relevant to corporate finance and capital budgeting rather than quantitative trading. It addresses investment project evaluation and payback period definitions, which are more applicable to long-term capital allocation decisions than to trading strategies. However, the axiomatic framework and mathematical rigor could inform risk management and project selection in institutional investment contexts.

The mathematical framework (locally bounded variation functions, Riemann-Stieltjes integrals, topological vector spaces) is sophisticated. However, the actual computation of the payback period PP(x) = inf{τ: x(t) ≥ 0 ∀t ≥ τ} is straightforward for discrete cash flows. The discounted payback period requires computing cumulative discounted cash flows via Riemann-Stieltjes integration. The axiomatic proofs are complex but the resulting formulas are simple to implement.

The paper is purely theoretical with complete mathematical proofs provided in the Appendix. All definitions, axioms, and propositions are formally stated and proven. No empirical data or computational experiments are required. The mathematical framework is self-contained and verifiable.