Solve entropic risk sensitive markov policy

Solve a finite-horizon Markov policy under exponential downside utility and compare it with the risk-neutral policy using paired Monte Carlo lower-tail CVaR.

What it's for

Prevents high-average recurring actions from winning when rare transition outcomes are catastrophic to the business.

What you give it

Inputs split into evidence read from your connected systems, calibration your team owns, and numerical controls that affect precision but never the result's meaning.

Field Type Role Required
actions array of objects (3 fields) ≥ 2 items Evidence Yes
horizon integer ≥ 2, ≤ 100 Your calibration Optional
initial_distribution object Evidence Yes
max_detail_rows integer ≥ 1, ≤ 2000 Numerical control Optional
risk_aversion number ≥ 0.000001, ≤ 20 Your calibration Optional
seed integer Numerical control Optional
simulations integer ≥ 200, ≤ 20000 Numerical control Optional
states array of objects (1 field) ≥ 2 items Evidence Yes
tail_probability number ≥ 0.01, ≤ 0.5 Your calibration Optional

Each actions record

Field Type Required
id string (non-empty) Yes
transition_probabilities object Yes
transition_rewards object Yes
Example input
{
  "actions": [
    {
      "id": "risky",
      "transition_probabilities": {
        "catastrophe": {
          "catastrophe": 0.5,
          "stable": 0.5
        },
        "stable": {
          "catastrophe": 0.05,
          "stable": 0.95
        }
      },
      "transition_rewards": {
        "catastrophe": {
          "catastrophe": -10,
          "stable": 0
        },
        "stable": {
          "catastrophe": -50,
          "stable": 5
        }
      }
    },
    {
      "id": "safe",
      "transition_probabilities": {
        "catastrophe": {
          "catastrophe": 0.1,
          "stable": 0.9
        },
        "stable": {
          "catastrophe": 0,
          "stable": 1
        }
      },
      "transition_rewards": {
        "catastrophe": {
          "catastrophe": -2,
          "stable": 0
        },
        "stable": {
          "catastrophe": -5,

Truncated for display — the full payload is 66 lines.

What you get back

This is the actual output of running the example above — computed by the same function the platform calls, not an illustration.

Example output
{
  "assumptions": [
    "States are Markov-sufficient, transition probabilities and transition rewards are stationary within the finite horizon, and rewards are commensurable and additive.",
    "Exponential utility represents constant absolute risk aversion; the declared coefficient governs downside sensitivity and must be approved by the decision owner.",
    "Entropic dynamic programming is time-consistent but is not the same objective as static CVaR; Monte Carlo lower-tail CVaR is reported as an interpretable audit cross-check.",
    "Policies govern reversible team, project, service, or portfolio actions and must not automate person-level employment or surveillance decisions."
  ],
  "decision": "risk_sensitive_policy_differs",
  "initial_value": {
    "risk_aversion": 0.1,
    "risk_neutral_expected_value": 8.6199,
    "risk_sensitive_certainty_equivalent": 4
  },
  "method": "finite_horizon_entropic_risk_sensitive_markov_control_v1",
  "policy": [
    {
      "period": 0,
      "policy_changed_by_tail_risk": true,
      "risk_neutral_action": "risky",
      "risk_sensitive_action": "safe",
      "state_id": "stable"
    },
    {
      "period": 0,
      "policy_changed_by_tail_risk": false,
      "risk_neutral_action": "safe",
      "risk_sensitive_action": "safe",
      "state_id": "catastrophe"
    },
    {
      "period": 1,
      "policy_changed_by_tail_risk": true,
      "risk_neutral_action": "risky",
      "risk_sensitive_action": "safe",
      "state_id": "stable"
    },
    {
      "period": 1,
      "policy_changed_by_tail_risk": false,
      "risk_neutral_action": "safe",
      "risk_sensitive_action": "safe",
      "state_id": "catastrophe"
    },
    {

Truncated for display — the full payload is 99 lines.

How it works

Markov & state-space control — Choose a policy over evolving states when today's action changes tomorrow's options.

  1. 1 Solve a finite-horizon Markov policy under exponential downside utility and compare it with the risk-neutral policy using paired Monte Carlo lower-tail CVaR.
  2. 2 Evaluate the method-specific diagnostics and gates returned by the function, then abstain unless the declared decision clears them under locally governed thresholds.

Before you trust it

Every tool in the catalog ships with the conditions under which its answer is meaningful — and the conditions under which it should abstain instead of guessing.

Assumptions & guardrails

  • States are decision-sufficient at the chosen cadence and transition evidence is recent, identifiable, and not silently pooled across incompatible regimes.
  • A policy is conditional on the declared state abstraction and transition model; hidden omitted state can invalidate its ranking.

Minimum evidence

  • states: at least 2 rows/items
  • actions: at least 2 rows/items
  • initial_distribution: required and organization-defined

How to validate it

Backtest the chosen action against simple feasible baselines on held-out scenarios, sweep costs/constraints/risk tolerance, and require constraint feasibility under adverse inputs.

Calibrating it to your org

Same for everyone

The mathematical kernel, validation rules, method version, and JSON output semantics are organization-independent; no tenant-trained coefficients or company benchmark is embedded in the function.

Specific to you

  • action-conditioned transition probabilities
  • transition-specific reward matrix
  • initial state distribution
  • state/action catalog
  • risk-aversion coefficient
  • reward valuation
  • horizon and lower-tail audit probability

Calibration workflow

  1. 1 Define the management decision, target outcome, aggregate unit, privacy boundary, cadence, and prediction/intervention horizon for this organization.
  2. 2 Build a tenant-scoped historical cohort using only information available before each prediction or decision; preserve zero periods, censoring, assignment probabilities, and unresolved outcomes when the method requires them.
  3. 3 Estimate statistical parameters on training history, but obtain costs, utilities, risk tolerance, practical-effect thresholds, capacity, and policy constraints from accountable decision owners.
  4. 4 Validate on later time windows or held-out aggregate units at the deployment grain, against a simple baseline and the function-specific validation strategy.
  5. 5 Deploy only if the returned decision clears evidence, overlap, calibration, robustness, and guardrail checks; warning, unsupported, schema-gap, and fallback decisions are abstentions.
  6. 6 Monitor realized outcomes, data drift, coverage, and decision regret; recalibrate at a governed cadence or after a detected regime/definition change, never merely because a stakeholder dislikes the result.

Call it from your AI

You don't wire up 388 tools in your MCP client. The GitRevio MCP server exposes 18 tools, three of which let an agent search the catalog, read a tool's schema, and run it — so the assistant finds this one on its own.

gitrevio_capabilities_search
  { "q": "solve a finitehorizon markov policy under" }
  → finds "solve_entropic_risk_sensitive_markov_policy"

gitrevio_capability_describe
  { "capability_id": "solve_entropic_risk_sensitive_markov_policy" }
  → returns the input schema and agent guidance shown on this page

gitrevio_capability_run
  { "capability_id": "solve_entropic_risk_sensitive_markov_policy", "arguments": { ... } }
  → returns the result shown above

Works in Claude Desktop, Claude Code, Cursor, Cline, Continue.dev, Goose and Aider. See the MCP server.

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