The selection of a best element from some set of available alternatives. Typically consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function.

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17
votes
5answers
11k views

What are some useful approximations to the Black-Scholes formula?

Let the Black-Scholes formula be defined as the function $f(S, X, T, r, v)$. I'm curious about functions that are computationally simpler than the Black-Scholes that yields results that approximate ...
23
votes
10answers
9k views

Why does the minimum variance portfolio provide good returns?

I've been a researching minimum variance portfolios (from this link) and find that by building MVPs adding constraints on portfolio weights and a few other tweaks to the methods outlined I get ...
7
votes
4answers
1k views

Library to solve optimization problems

I'm working with C# and I start being bored writing optimization algorithm. Do you know of any free library containing this sort of algorithms. In particular I'm cutrently working with Semidefit ...
2
votes
1answer
87 views

How to apply Levenberg Marquardt to Max Likelihood Estimation

In this paper on p315: http://www.ssc.upenn.edu/~fdiebold/papers/paper55/DRAfinal.pdf They explain that they use Levenberg Marquardt (LM) (along with BHHH) to maximize the likelihood. However as I ...
2
votes
1answer
218 views

What is the difference between these two optimization procedures?

In this portfolio optimization utility (and others), mean return, standard deviation and correlation among assets are required inputs. http://finance.wharton.upenn.edu/~stambaugh/portopt.html At ...
16
votes
6answers
7k views

Python library for Portfolio Optimization

Does anyone know of a python library/source that is able to calculate the traditional mean-variance portfolio? To press my luck, any resources where the library/source also contains functions such as ...
15
votes
1answer
960 views

Portfolio optimization with monte carlo sampling from predictive distribution

Let's say we have a predictive distribution of expected returns for N assets. The distribution is not normal. We can interpret the dispersion in the distribution as reflection of our uncertainty (or ...
4
votes
2answers
402 views

Choice of prior as a shrinkage target in portfolio construction?

There's various research showing how priors such as the minimum variance portfolio turn out to be a surprisingly effective shrinkage target in portfolio construction. The sell point of these priors ...
5
votes
1answer
276 views

Min VaR and Min TE as second order cone program

The quadratic optimization (min variance) $$ w^{T} \Sigma w \rightarrow \text{min}, $$ where $w$ is the vector of portfolio weights and $\Sigma$ is the covariance matrix of asset returns, is a well ...
6
votes
2answers
838 views

Comparing MVO with Resampled Efficient Frontier

My question: How can I compare the Resampled Frontier (REF) to the standard MVO frontier when I have been provided with $\mu$, $\Omega$, and don't have access to true future data to test real out of ...
5
votes
1answer
1k views

Optimizing a portfolio of ETFs

I am aware of how to do mean-variance or minimum-variance portfolio optimization with constraints like weights must add to 1.0 no short sells max weight in any ticker using basic quadratic ...
4
votes
0answers
201 views

Optimization: Factor model versus asset-by-asset model

In portfolio management one often has to solve problems of the quadratic form $$ w^T \Sigma w + w^T c \rightarrow Min $$ with portfolio weights $w \in \mathbb{R}^N$ a constant $c \in \mathbb{R}^N$ and ...
4
votes
0answers
290 views

Shrinkage Estimator for Newey-West Covariance Matrix

I like to apply the Newey-West covariance estimator for portfolio optmization which is given by $$ \Sigma = \Sigma(0) + \frac12 \left (\Sigma(1) + \Sigma(1)^T \right), $$ where $\Sigma(i)$ is the lag ...