# Portfolio Construction with Gaussian Mixture Returns and Exponential Utility via Convex Optimization

@article{Luxenberg2022PortfolioCW, title={Portfolio Construction with Gaussian Mixture Returns and Exponential Utility via Convex Optimization}, author={Eric Luxenberg and Stephen P. Boyd}, journal={SSRN Electronic Journal}, year={2022} }

We consider the problem of choosing an optimal portfolio, assuming the asset returns have a Gaussian mixture (GM) distribution, with the objective of maximizing expected exponential utility. In this paper we show that this problem is convex, and readily solved exactly using domain-speciﬁc languages for convex optimization, without the need for sampling or scenarios. We then show how the closely related problem of minimizing entropic value at risk can also be formulated as a convex optimization…

## References

SHOWING 1-10 OF 52 REFERENCES

### Portfolio optimization when asset returns have the Gaussian mixture distribution

- Computer ScienceEur. J. Oper. Res.
- 2008

### Portfolio Optimization within Mixture of Distributions

- Economics
- 2014

The recent financial crisis has highlighted the necessity to introduce mixtures of probability distributions in order to improve the estimation of asset returns and in particular to better take…

### Optimal Portfolio Allocation Under Higher Moments

- Economics
- 2004

We evaluate how departure from normality may affect the allocation of assets. A Taylor series expansion of the expected utility allows to focus on certain moments and to compute numerically the…

### Entropic Portfolio Optimization: A Disciplined Convex Programming Framework

- Computer Science
- 2021

This work presents a disciplined convex programming framework for entropic value at risk (EVaR) based on exponential cone programming, and proposes a new portfolio optimization framework based on an extension of EVaR but applied to drawdowns distribution.

### Efficient Portfolio Selection with Quadratic and Cubic Utility

- Economics
- 1970

Decisions about investment, or portfolio selection, are regarded as choices among alternative probability distributions of returns, where the optimal choice is determined by maximization of the…

### Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case

- Economics
- 1969

OST models of portfolio selection have M been one-period models. I examine the combined problem of optimal portfolio selection and consumption rules for an individual in a continuous-time model…

### Convex Optimization

- Computer ScienceIEEE Transactions on Automatic Control
- 2006

A comprehensive introduction to the subject of convex optimization shows in detail how such problems can be solved numerically with great efficiency.

### Minimizing oracle-structured composite functions

- Computer ScienceOptimization and Engineering
- 2022

A method that makes minimal assumptions about the two functions, does not require the tuning of algorithm parameters, and works well in practice across a variety of problems, showing that the method is more efficient than standard solvers when the oracle function contains much data.

### Multi-Period Trading via Convex Optimization

- EconomicsFound. Trends Optim.
- 2017

A framework for single-period optimization, where the trades in each period are found by solving a convex optimization problem that trades off expected return, risk, transaction cost and holding cost such as the borrowing cost for shorting assets.

### Entropic Value-at-Risk: A New Coherent Risk Measure

- Computer ScienceJ. Optim. Theory Appl.
- 2012

It is shown that a broad class of stochastic optimization problems that are computationally intractable with the CVaR is efficiently solvable with the EVaR, and it is proved that if two distributions have the same EVsaR at all confidence levels, then they are identical at all points.