# Optimal consumption of multiple goods in incomplete markets

## TL;DR

This paper investigates the problem of optimal consumption across multiple goods within incomplete markets, providing dual formulations, existence and uniqueness conditions, and explicit solutions in certain models.

## Contribution

It introduces a dual problem framework for multiple goods consumption in incomplete markets and derives conditions for solution existence and uniqueness, including closed-form solutions in some cases.

## Key findings

- Established dual problem formulation for incomplete markets
- Derived conditions for existence and uniqueness of optimal consumption
- Constructed closed-form solutions in specific incomplete market models

## Abstract

We consider the problem of optimal consumption of multiple goods in incomplete semimartingale markets. We formulate the dual problem and identify conditions that allow for existence and uniqueness of the solution and give a characterization of the optimal consumption strategy in terms of the dual optimizer. We illustrate our results with examples in both complete and incomplete models. In particular, we construct closed-form solutions in some incomplete models.