Quantitative Retirement Optimization Engine
Praxion is a tax-aware financial optimization platform that models multi-account retirement decumulation under deterministic cash-flow constraints and stochastic return processes.
The platform integrates:
- Deterministic tax modeling
- Constrained withdrawal optimization
- Dynamic Roth conversion modeling
- Monte Carlo return simulation
- Specialized AI agents and LLM orchestration (runtime), grounded in the same engine
- AI-assisted scenario exploration and strategy comparison
- Multi-objective strategy scoring
It operates as a year-indexed state transition engine across a full retirement horizon, designed for precision, transparency, and robustness.
1. Mathematical Framework
1.1 State Vector Definition
At time t, the household financial state is defined as:
St = [ Attrad, Atroth, Atbroker, Btbasis, Itss, Itother, τt ]
Where:
- Attrad: Traditional tax-deferred balance
- Atroth: Roth balance
- Atbroker: Taxable brokerage balance
- Btbasis: Cost basis
- Itss: Social Security income
- Itother: Other income
- τt: Tax bracket regime
The system evolves via:
St+1 = f(St, Wt, Rt, Ct)
Where:
- Wt: Withdrawal vector
- Rt: Return vector
- Ct: Conversion decision
2. Deterministic Cash-Flow Engine
The deterministic layer computes annual net cash flow:
CFt = Wttrad + Wtroth + Wtbroker + It − Tt
Taxes are computed via Tt = g(Ytordinary, Ytcapital). Ordinary income includes traditional withdrawals, Social Security taxable portion, and RMD distributions. Capital income includes realized gains and qualified dividends.
Tax function g is piecewise progressive and parameterized by federal brackets, state brackets, IRMAA thresholds, net investment income surtax (NIIT), and RMD schedules.
3. Withdrawal Optimization
The withdrawal vector Wt = [ wttrad, wtroth, wtbroker ] is determined by rule-based, intent-driven logic. Each year, the engine satisfies cash flow needs and RMD requirements, then applies ordering and conversion rules keyed to user intent (e.g. minimize taxes, balanced, stable income). Constraints enforced:
- Cash flow constraint (expenses and taxes must be funded)
- RMD constraint (required minimums from traditional accounts)
- Non-negativity and account balance continuity
- Tax bracket and IRMAA awareness
Strategies implemented include bracket-filling, RMD pressure reduction, Roth conversion front-loading, and IRMAA cliff avoidance. Withdrawal order (brokerage vs traditional vs Roth) and conversion amounts are chosen by the policy engine and dynamic optimizer, not by a single formal objective function.
4. AI Agents, LLMs, and Scenario Exploration
4.1 Runtime: specialized AI agents
At runtime, Praxion uses multiple specialized AI agents coordinated with large language models (LLMs). Multiple product-facing agents—AI Review, AI Optimizer, Data Health, and Praxion AI—each focus on a different job: exhaustive strategy and conversion testing, market-aware shock response and validated adjustments, keeping account balances and projections aligned with live market drift, and answering your questions conversationally against the same engine. They operate through a Generator–Critic architecture: one model (or step) proposes concrete changes, and an independent critic validates proposed changes against guardrails before anything is shown as actionable—typically with structured feedback and limited refinement iterations when proposals are rejected.
What the LLM does not do: it does not replace the tax, cash-flow, or Monte Carlo code. Agent outputs are grounded in tool calls and API-backed runs against the same deterministic engine described in sections 1–3 and 5–7. Numbers you see from those features come from executed projections, not from free-form model arithmetic.
For a product-level walkthrough, see AI Capabilities. For a longer technical narrative — including the canonical mapping of the five backend agents (Tax Strategy, Shock Simulation, Withdrawal Sequencing, Data Health, Critic) onto the AI Review, AI Optimizer, and Data Health UI surfaces named above — see How AI Agents Optimize Your Retirement Plan. For a deep dive into the agent runtime infrastructure — capability planes, multi-model provider support, observability, and governance — see Agent Fabric: How Praxion Orchestrates AI Agents at Scale.
4.2 Praxion AI (conversational interface)
Praxion AI is a conversational layer that can invoke the retirement stack through defined tools (e.g. projections, analyses, and comparisons) so answers stay tied to your profile and our engine, rather than generic LLM-only opinions. The same separation applies: conversational reasoning is layered on top of auditable computation. For positioning vs. general-purpose chatbots, see Praxion AI: Redefining Financial Intelligence.
4.3 Scenario exploration and analysis
The product explores multiple strategy and scenario variants: different Roth conversion strategies, withdrawal modes (e.g. dynamic tax-optimized, policy-based, static), and fixed or percentage withdrawal rules. Strategy comparison runs several strategies and withdrawal modes against the same profile and scores them. Stress tests and reference-profile comparisons use a fixed set or a single synthetic profile to validate the engine. Core tax, cash-flow, and Monte Carlo logic remains deterministic and auditable; agents and LLMs orchestrate and explain comparisons—they do not silently substitute for that logic.
5. Monte Carlo Risk Engine
Returns Rt are sampled from a multivariate distribution (e.g. Rt ∼ N(μ, Σ) or regime-adjusted). Each strategy is simulated across N paths; metrics evaluated include:
- Survival probability
- P10 / P50 / P90 terminal wealth
- Tax volatility
- Drawdown magnitude
- Income shortfall probability
Sequence-of-returns risk is explicitly modeled through time-indexed sampling.
6. Account-Level Tax Modeling
Brokerage accounts are decomposed as Atbroker = Btbasis + Gtunrealized. Capital gains realized during withdrawals: CGt = wtbroker · Gtunrealized / Atbroker.
Social Security taxation follows provisional income thresholds: PIt = AGIt + 0.5 · SSt. RMD calculations follow IRS life expectancy tables: RMDt = Attrad / LEt.
7. Multi-Objective Strategy Scoring
Strategies are scored using a fixed composite: lifetime tax (25%), terminal wealth / final assets (30%), RMD impact (30%), and success probability (15%). Lower tax and lower RMD impact improve the score; higher final assets and higher success rate improve it. The comparator ranks strategies by final assets with this composite as a tiebreaker. Tax-optimization and strategy-comparison features use this scoring to suggest a strategy and withdrawal mode for comparison.
Intent-aligned (paper) scoring. We also support an optional scoring formula that aligns with a formal objective: discounted lifetime tax plus a penalty for income volatility (Σ βt Tt + λ·Variance(cash flow)). When your intent is stable income, strategies with smoother annual cash flow rank higher; the comparator can use this formula so the suggested strategy reflects both tax efficiency and income stability. We run internal before/after comparisons (legacy composite vs. paper-aligned ranking) and generate reports to validate and explain the analysis. When both rankings agree, the improvement is in the formula and in how alternative strategies are ordered—smoother options rank higher even if the top pick is unchanged; when they disagree, the paper-aligned ranking favors the smoother strategy when it is close on tax and assets.
8. Model Validation & Verification
Validation uses a mix of synthetic and reference household profiles: high-income and bracket-compression cases, early retirement and Roth-heavy strategies, low-income and Social Security–focused cases, RMD-heavy late retirement, capital gains threshold edge cases, and IRMAA boundary scenarios. Checks include deterministic cash-flow correctness, tax liability benchmarks, withdrawal sequencing outcomes, cross-year state continuity, and Monte Carlo stress-test consistency. Regression and reference-profile comparison tests are run when tax or core logic changes to validate correctness.
9. System Architecture
Conceptual data flow:
┌────────────────────────┐
│ User Inputs │
│------------------------│
│ Assets │
│ Income Streams │
│ Tax State │
│ Goals & Constraints │
└──────────┬─────────────┘
│
▼
┌────────────────────────────┐
│ LLM & AI Agent Layer │
│----------------------------│
│ Praxion AI (tools → API) │
│ AI Review / AI Optimizer / │
│ Data Health (Generator– │
│ Critic, orchestration) │
└──────────┬─────────────────┘
│
▼
┌────────────────────────────┐
│ Deterministic Engine │
│----------------------------│
│ Year-by-Year Cash Flow │
│ Tax Bracket Engine │
│ RMD Module │
│ SS Taxation Model │
└──────────┬─────────────────┘
│
▼
┌────────────────────────────┐
│ Withdrawal Optimizer │
│----------------------------│
│ Bracket Filling Logic │
│ Conversion Engine │
│ Constraint Solver │
└──────────┬─────────────────┘
│
▼
┌────────────────────────────┐
│ Strategy & Scenario Engine │
│----------------------------│
│ Strategy Comparison │
│ Withdrawal Mode Variants │
│ Conversion / Edge-Case Eval │
└──────────┬─────────────────┘
│
▼
┌────────────────────────────┐
│ Monte Carlo Engine │
│----------------------------│
│ Return Sampling │
│ Path Simulation │
│ Risk Scoring │
└──────────┬─────────────────┘
│
▼
┌────────────────────────────┐
│ Strategy Comparator │
│----------------------------│
│ Lifetime Tax │
│ Survival Rate │
│ Income Stability │
│ Terminal Wealth │
└────────────────────────────┘10. Design Principles
- Deterministic transparency before stochastic modeling
- Explicit tax logic with full auditability
- AI agents and LLMs orchestrate analysis; the engine stays auditable—not a black box
- AI-assisted scenario exploration with outcomes tied to executed engine runs
- Continuous validation with varied household profiles
- Multi-objective optimization for tax, longevity, and income stability
Tech Stack & Implementation
Praxion Finance runs on a split-stack architecture designed for reliability and scale.
- Frontend: A modern component-based JavaScript framework with interactive data visualizations.
- Backend API: All retirement math—projections, tax logic, withdrawal sequencing, Monte Carlo—runs server-side so results are consistent and auditable.
- Data: A managed cloud database accessed through a unified data layer. Data is encrypted at rest.
- Auth: A managed identity provider with support for federated (single) sign-in and multi-factor authentication.
- Infrastructure: Hosted on a major cloud provider with managed compute, storage, and monitoring. A content delivery network and web application firewall sit in front of the application, with modern TLS for transport security.
- AI runtime: LLM-backed agent flows (orchestration, Generator–Critic steps, and conversational tool use) call the same backend APIs as the rest of the product so numerical results stay consistent with the deterministic engine.
Calculations are not done in the browser: your numbers are sent to our API, processed by the same engine that passes our stress tests, and returned as projections and analysis. This keeps logic centralized and verifiable.
AI-Built, Human-Verified (engineering)
This section is about how we build software, distinct from the runtime AI agents in section 4. A significant portion of the platform was implemented using LLM-assisted development with Cursor.com. Requirements and logic were defined by humans; implementation and iteration were accelerated by AI, with code review, testing, and stress runs used to verify correctness.
We do not claim "every line written by AI" in a literal sense—rather, the development process is AI-assisted and the codebase is continuously refined with human oversight. Mathematical and tax rules are validated against known cases and our own stress tests. For more on mission and philosophy, see our About page.
Stress Testing & Validation
Our Monte Carlo engine is the same in production and in our stress tests. We ran it through 100,000 scenarios with extreme, low-probability ("Black Swan") assumptions to ensure the engine does not crash and produces valid, finite outputs under severe conditions.
Stress-test parameters include mean return -3%, volatility 35%, and elevated inflation assumptions to simulate tail events. Under these assumptions, a low success rate is expected; the goal is zero logic failures and valid outputs on every run. We also run retirement stress-test profile comparisons against reference profiles to validate projection behavior across varied household types.
Security & Privacy
We use a siloed architecture: your financial data is processed in a secure, isolated context and is not used to train public or third-party AI models. For full details, see our Security & Privacy page.
As stated there: we use industry-standard practices including strong encryption in transit and encryption at rest, provided by the security controls of our hosting and database providers. Passwords are protected with industry-standard one-way hashing; sessions are validated on every authenticated request; and the API applies common hardening measures such as request rate limiting and secure HTTP response headers.
We do not sell your personal or financial information. For data collection, use, and your rights, see our Privacy Policy.
Ready to Plan with Purpose?
Use the same engine we stress-test—for your own retirement plan.
Start Free