# Classical regularity and attainment in portfolio choice with nonhomothetic utility

## Files

- `manuscript.tex`: complete LaTeX source, including appendices and references.
- The compiled PDF is generated by Hexagon from `manuscript.tex`.
- `anc/identities.py`: exact symbolic calculations accompanying the proofs.
- `anc/requirements.txt`: tested Python dependency.

Authors (in citation order): Yuanhong Wei; Zhenyu Sun.

Yuanhong Wei: School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao, Hebei Province, China. Email: 202410074@stu.neuq.edu.cn. ORCID: https://orcid.org/0009-0009-8029-5964. No empirical dataset is used in this theoretical study.

## Compile

From this directory, use a TeX installation with pdfLaTeX and the standard packages loaded in the source:

```sh
latexmk -pdf -interaction=nonstopmode -halt-on-error manuscript.tex
```

Alternatively, run pdfLaTeX three times to resolve cross-references:

```sh
pdflatex -interaction=nonstopmode -halt-on-error manuscript.tex
pdflatex -interaction=nonstopmode -halt-on-error manuscript.tex
pdflatex -interaction=nonstopmode -halt-on-error manuscript.tex
```

The source includes its bibliography and needs no external chapter or image files. The Latin Modern fonts are supplied by the TeX distribution.

## Symbolic calculations

Use Python 3.10 or later. From this directory:

```sh
python -m pip install -r anc/requirements.txt
python anc/identities.py
```

The dependency is pinned to the tested version of SymPy. The script needs no dataset, random seed, external file, or network access. It exits with a nonzero status if any symbolic residual is nonzero. A successful run ends with:

```text
All 57 exact algebraic calculations returned zero residual.
```

The calculations cover the marginal and gradient equations, principal matrices, nonsymmetric fluxes, optimal density identities, utility transformations, commutator-scaled auxiliary markets, opportunity-clock derivatives, moment boundaries, and the replication energy identity. The multidimensional checks use three traded risks and two factors with symbolic covariance entries. The general-dimensional arguments and the analytic and stochastic proofs are contained in the manuscript.

## AI-assisted language editing

ChatGPT was used for proofreading and language editing. The authors retain responsibility for the content of the manuscript.