Engines A & B

ArcLogic splits portfolio work into a strategic layer (Engine A) and a tactical layer (Engine B). They share a philosophy — transparent inputs, inspectable outputs — but use different math because they answer different questions.

Engine A — Strategic baseline

Financial BMR (baseline maintenance return) is the “maintenance calories” idea for wealth: the blended return the invested slice of the book must target so withdrawals can keep pace with inflation and stated lifestyle drift, after you account for cash that earns a risk-free (or near–risk-free) rate. In code, spend is annual spend; implied burn is annualSpend / netWorth; the real spending hurdle is inflation + lifestyle creep (both as annual decimals, e.g. 0.03 and 0.01). The engine solves for a single maintenance return on the equity slice when cash is carved out.

Linear projection compounds an initial value at a net expected annual return and optional end-of-year contributions — a deliberate simplicity for roadmap and sufficiency questions, not a market model.

Gap diagnostics (yield gap) compute how much extra annual funding closes a shortfall between where the linear path lands and a target, given a fixed horizon and expected return. It answers “how much more do I need to put in per year?” when you are not on track.

Engine B — Tactical reality

Monte Carlo (tactical stress) in the lab uses a geometric-Brownian-style annual step: each year, return is mean + volatility × z for a standard normal z, applied to wealth. The output distribution (e.g. P25 / P50 / P75 of terminal wealth) is a shape tool — it shows dispersion under your stated mean and vol — not a claim that real markets are lognormal or that one vol number captures tail risk. A fixed seed makes runs reproducible for side-by-side comparison.

Greeks and surfaces use the Black–Scholes framework: d₁, d₂ as usual, call delta Δ = N(d₁), and the standard closed forms for gamma, vega, and theta. The heatmaps plot these against strike and days-to-expiry for a given spot, rate, and implied vol. Theta is expressed in $/day per one share of underlying in the notional; vega in the engine is per a 1.0 move in σ (i.e. 100 vol points) unless you scale — check the exact panel label in the app when you trade live size.

Theta education curve in the library uses a simple sqrt(DTE) scaling from a reference premium to illustrate time shape; it is not a substitute for full term-structure or dividend-aware pricers.

Where to go next

Strategies & lab covers defined-risk P/L at expiry and how those formulas map to the call credit spread and iron condor payoffs in the product.