[markov_asset] Update to JAX and runtime comparison

[xuanguang-li]

This pull request modernizes the markov_asset.md notebook by refactoring the codebase to use JAX and JAX NumPy.

• Refactored all numerical computations and linear algebra from numpy and numpy.linalg to jax.numpy and jax.numpy.linalg.
• Replaced the mutable AssetPriceModel class with an immutable, type-safe NamedTuple version and introduced a create_ap_model factory function for consistent construction.
• Updated function signatures and internal logic to use the new model structure.
• Replaced manual Python loops with JAX functional control flow constructs such as jax.lax.while_loop and jax.lax.fori_loop.
• Fixed minor bugs in parameter initialization, state handling, and tolerance defaults.

Update: Runtime Comparison Between JAX (GPU), JAX (CPU), and NumPy

Methodology:

• The JAX version uses the code in this PR, while the NumPy version uses the code in main.
• The runtime for JAX (GPU) is measured using Google Colab.
• Runtime is collected using qe.timeit over 1,000 iterations.
• Each iteration consists of one function that solves the consol price and one that solves the call option price.

Results:

• Average runtime: JAX (CPU) > NumPy > JAX (GPU).
• More details are shown in the attached plots.

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[jstac]

🤖 Status note for a future session — from a maintainer investigation on 2026-07-08 into why open-PR previews 404. Context only, not instructions.

Netlify preview: https://pr-654--sunny-cactus-210e3e.netlify.app/ currently returns 404.

Why previews are down (repo-wide findings)

1. This branch is stale — 164 commits behind main. A preview build compiles the whole site from this branch. This branch's lectures/house_auction.md still has unpinned !pip install prettytable, which now breaks on a wcwidth incompatibility. main fixed this on 2026-06-28 by pinning prettytable<3.18 (#939). This alone fails any rebuild of this branch until it's updated to main.

2. The arviz failure was a red herring — do NOT pin arviz or rewrite plotting. A 2026-07-07 rebuild also failed in ar1_bayes/ar1_turningpts with an arviz_plots figsize ValueError. That was a transient bug in an intermediate arviz-plots 1.x release, already fixed in arviz 1.2.0. Verified locally on a clean latest-stack venv: the real az.plot_trace(trace) cell (pymc + numpyro InferenceData) runs green. The lectures use only 1.x-compatible arviz APIs (plot_trace, summary, from_numpyro, compare).

Note on recent timeline activity

This PR was close/reopened on 2026-07-07 by a maintainer session purely to trigger a rebuild test — not a content change. That rebuild failed on the stale-branch issue above. Apologies for the notification churn.

Recommended first step for this PR

Update this branch to main (merge or rebase — pulls in #939 plus ~164 other commits), then let CI rebuild. On today's latest libraries the site builds clean, so the preview should return. house_auction is the known blocker; updating also picks up other since-merged fixes — rebuild and address any remaining per-lecture failures. Verify with:

curl -sI https://pr-654--sunny-cactus-210e3e.netlify.app/markov_asset.html

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This PR touches: markov_asset.md, markov_asset_numpy.md. Last CI build: failure@2026-07-07. Branch: 164 commits behind main as of 2026-07-08.

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• markov_asset
• markov_asset_numpy

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Build Info

• Workflow: Build Project [using jupyter-book]