Convex Risk Measures for Acceptable Portfolio Wealth

Summary

The document describes a computational approach for a trader seeking portfolio wealth outcomes that satisfy a convex risk measure. The proposed black-box method takes the joint distribution of stock prices and the chosen risk measure as inputs, then calculates the required initial capital and gives the functional form of a trading strategy intended to achieve acceptability.

It also states that the capital requirement produced by the method is optimal. The excerpt does not specify the algorithm’s steps, assumptions about trading constraints, the kinds of risk measures supported, or numerical examples. Those details would be needed to assess implementation and practical performance.

Key ideas

• A convex risk measure can define which portfolio wealth outcomes count as acceptable.
• The proposed algorithm uses the joint law of stock prices and a risk measure as inputs.
• Its outputs include required initial capital and a trading strategy’s functional form.
• The document claims the calculated capital requirement is optimal.

Tags

# Computing strategies for achieving acceptability


# Computing strategies for achieving acceptability









We consider a trader who wants to direct his portfolio towards a set of acceptable wealths given by a convex risk measure. We propose a black-box algorithm, whose inputs are the joint law of stock prices and the convex risk measure, and whose outputs are the numerical values of initial capital requirement and the functional form of a trading strategy to achieve acceptability. We also prove optimality of the obtained capital.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.