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Questions tagged [optimization]

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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Formula for the efficient portfolios in mean-variance optimisation?

Consider the setting of mean-variance portfolio optimisation: $n$ assets with expected returns $\overline{r}_1,...,\overline{r}_n$ and standard deviations $\sigma_1,...\sigma_n$. For a certain fixed $\...
Phil-ZXX's user avatar
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7 votes
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Is there a standard method of scaling alpha forecasts to t-cost estimates?

Given a set of monthly alpha forecasts (i.e. standardized z-scores from a multi-factor return model) and a non-linear market impact model (or more specifically, its piecewise-linear approximation), is ...
michaelv2's user avatar
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6 votes
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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 ...
Richi Wa's user avatar
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5 votes
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Optimized search for yield-to-worst of a callable bond

Suppose that I need to find the yield-to-worst of a callable bond, and that the option is American (call any time). The bond may have step-up coupons and/or non-constant call price (oprion strike). ...
Dimitri Vulis's user avatar
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Fitting GARCH(1,1) in Python for moderately large data sets

I am using the arch package in python to fit a GARCH(1,1) to fit daily S&P 500 returns from 1990 to 2017 (about 6800 data points). The code I am using is as follows: ...
user369210's user avatar
5 votes
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154 views

Optimal mortgage rate strategy

When buying a mortgage, you can choose to "lock in" a rate at any point within 60 days of your closing date. Once locked in, you can't revert. This makes it a secretary problem - in the traditional ...
Xodarap's user avatar
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5 votes
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Analyzing the angle between vector of weights and vector of returns in mean-variance optimization

I am using the paper "A Sharper Angle on Optimization" by Golts and Jones (2009) as a basis for my (minor) masters thesis in mathematical finance. The paper focuses on the mean-variance analysis of ...
Geraldine Bailey's user avatar
4 votes
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How would it be possible to use Dynamic Programming to search a space of investment strategies to find an optimum?

As my question states, the problem I am having is finding a sensible way to search a large space. Any help or insight that could be provided would be hugely appreciated. Currently I am trying to ...
ahair's user avatar
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3 votes
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309 views

Which C++ implementations of Levenberg-Marquardt does the "industry" use?

According to your various experience, is there an industry consensus about which C++ implementation of the Levenberg-Marquardt algorithm to use ? I came across two places where it was the C numerical ...
EricFlorentNoube's user avatar
3 votes
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Linear programming optimization problems in finance

I'd like to know what are, if any, the applications of linear/non linear programming optimization techniques for financial markets. I'm a business major, and I want to find an argument for my thesis ...
Francesco Totti's user avatar
3 votes
1 answer
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Has work been done on PID controllers for optimal trading?

Commonly, stochastic control is the basis for optimal trading (either in execution or market-making). Has any research been done (or why not, if none) as to PID controllers for these applications?
Kch's user avatar
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Fitting High Frequency Indicators

I have a high frequency time series of the bid and ask prices of a stock recorded on every tick. For each data point I also have a certain indicators that predict the future movement of the price. The ...
algotr's user avatar
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3 votes
0 answers
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Residual Covariance Matrix, and MVO for Residual Variance and Alpha

My overall goal is to find an efficient frontier using QP in terms of $\alpha$ and residual variance ($\omega^2$) for a portfolio $P$ given a benchmark $B$. We know the equation for residual variance ...
MarkD's user avatar
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State Space models with Short Time Series

My problem is that I have a state space model that I estimate using the Berndt–Hall–Hall–Hausman (BHHH) algorithm. The state space model is relatively simple in that the hidden part follows a pure AR(...
Bazman's user avatar
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What R-packages for SOCP problems are there?

Currently, I am looking deeper into the topic of second-order cone programming. Could you suggest packages that solve SOCP-problems in R? With your answer, please provide a short description of ...
vanguard2k's user avatar
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A doubt about Evans and Jovanovic (1989) economic model for entrepreneurs with credit constraints

[I already posted this question on the math forum of stackexchange and I was advised that I should post this question here] In Evans and Jovanovic (1989) you will find a model for entrepreneurs with ...
John Doe's user avatar
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Optimizing stochastic functions numerically

Is there an efficient and commonly used optimization method for "more complex" investment strategies. For instance, say you have a function $f(X_1,...,X_n,c,v)$ where the $X_k$'s are your random ...
Good Guy Mike's user avatar
3 votes
0 answers
204 views

Opimization on a Bond Portfolio

...
gabriel's user avatar
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2 votes
0 answers
129 views

Optimal consumption process [Munk (2011)]

I'm trying to solve problem 4.4 in Munk (2011). The problem is as follows: Assume the market is complete and $\xi = (\xi_{t})$ is the unique state-price deflator. Present value of any consumption ...
John Stevens's user avatar
2 votes
0 answers
197 views

Can genetic algorithm help in portfolio optimisation when convexity is not verifiable

I have the following portfolio cost function to maximise: $$ w^T\mu-\frac{1}{2}\gamma w^T\Sigma w+\frac{1}{6}\gamma^2 w^TM_3(w\otimes w), $$ which considers the co-skewness ($M_3$ tensor), $γ$ is the ...
Luigi87's user avatar
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How to optimize a non-linear least squares problem with cvxpy/cvxopt

I know how to minimize a linear function $f : \mathbb{R}^{n} \rightarrow \mathbb{R}$ with CVXPY but in my problem the function $f$ is quadratic and hence the problem is now in the form : $$\lVert AW-...
FredNgu's user avatar
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392 views

Transform this non-linear portfolio optimization problem into a quadratic optimization problem

I have a portfolio optimization problem similar to this question here, with a V-shape transaction costs such that we pay a fee proportionally to the sum of absolute rebalancing: $$TC(\omega) = \frac{1}...
JejeBelfort's user avatar
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Interchange Expectation and Supremum in Snell Envelope/American Options

I had a question about the properties of a snell envelope, $\sup_{t\le\tau\le T} \Bbb E\left(Z_\tau\mid \mathcal F_t\right)$, which came to me while studying American options. I know that in general,...
Slade's user avatar
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2 votes
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232 views

Bootstrapping and Curve Calibration Objective Function

I'm confused about the form of the objective function for some global curve calibration. It seems simple enough: minimized the squared loss of the price of the input instruments and the price ...
moquant's user avatar
  • 115
2 votes
0 answers
259 views

Optimisation problem with bid-ask spread

I want to optimise a static portfolio with a holding period of 90 days given 10 tradable assets. The assets are quoted in bid and ask prices. I want to minimise the risk measured by standard deviation ...
quallenjäger's user avatar
2 votes
0 answers
726 views

Optimal weights for portfolio optimisation (r)

The question is what R optimization could be applicable to find a vector of weights that when, multiplied by S matrix creates equal rows sums, and when set in the objective function returns the ...
user2948605's user avatar
2 votes
0 answers
174 views

Using Market Prices of Bonds to Model the Discount Curve with a Polynomial (Math + R)

I have a small program I'm building to interpolate the discount curve from a portfolio of benchmark bonds. If anyone has any guesses as to whether it's my process, or my code that's messed up I would ...
user3338639's user avatar
2 votes
0 answers
59 views

Given (past) stock values for N assets, how to find the maximum - theoretical - profit?

In the past few days I have been thinking about a question which seems trivial, yet I can't think of any efficient way to find the optimal solution... Here is the problem: imagine you have a ...
Federico's user avatar
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101 views

robust regions in grid search

I have a strategy f that takes parameters x,y (for x,y taking values in integer ranges). I get two grids (of returns and volatility values) from computing f(xi,yi) for integer ranges x1 <= xi <= ...
KS1's user avatar
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portfolio optimization with a loop

I am attempting to minimize the variance of a 3 stock portfolio using optimization within a loop. What I have done is calculated the stock returns and cov matrix from dates 1980-01-01 to 1989-12-31 ...
user2214069's user avatar
1 vote
0 answers
27 views

Implicit function theorem and sensitivities to market risk for Nelson-Siegel-Svensson model

I’m calibrating the Nelson-Siegel-Svensson model to market rates and I’m trying to compute the sensitivities of the NSS parameters to those said rates: $$r\left(T\right)=\beta_{0}+\beta_{1}{\frac{\...
loyd.f's user avatar
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1 vote
0 answers
53 views

Am I overcomplicating this approach to optimal actions based on a forecast?

I have been attempting to implement a simplified version of the model used in this paper which, given a forecast of future data, provides an optimal way of acting on it by choosing an optimal sequence ...
QMath's user avatar
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1 vote
0 answers
33 views

Duality in conic quadratic programming for good deal measure

I am working on a problem relating to what is known as the "Good Deal risk measure" for production valuation in incomplete markets. I have created the following primal optimization problem, ...
Mikkel Honningsvåg Sandhaug's user avatar
1 vote
0 answers
203 views

Calibration of $\rho$ in the heston model

When calibrating the Heston model, the gradient of the price of the call/cost function wrt $\rho$ (correlation between $S$ and $V$), is a lot less than the other parameters like $v_0$ and $\bar{v}$. ...
THATS MY QUANT MY QUANTITATIVE's user avatar
1 vote
0 answers
89 views

Optimal portfolio as combination of target and minimum tracking error portfolios?

Dear Quant StackExchange I seek some intuition for how my portfolio behaves given constraints. In a universe of say 5 assets, I have a "target portfolio" with weights that are found from ...
fdp1996's user avatar
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1 vote
0 answers
159 views

SciPy Calibrating Heston call option

I have been attempting to calibrate my Heston model, but I am running into issues with scipy.optimize module. I have tried various scipy optimizers, but they all return the error "TypeError: can ...
DiracsCallOption's user avatar
1 vote
0 answers
139 views

MatLab code does not work for Heston model calibration

I am trying to calibrate Heston model on some data and I have the following code. Code is supposed, after it reads the data, to give back 5 parameters. However, I get an empty answer from MatLab. Does ...
Francesco Bova's user avatar
1 vote
0 answers
133 views

An example that mixes the stock market, game theory and linear programing

First of all i am not entirely sure if this is the correct place to discuss this problem but i shall give it a try. I'm currently doing an assignment for a degree in Linear Programing. My objective ...
riemannfanboy's user avatar
1 vote
0 answers
27 views

Interest Expense Optimization

So I have a problem I need to solve and no idea how to approach it. Its a verbal problem without any specific numbers given except for those below. So it is up to me to determine how to structure the ...
thenoobie's user avatar
1 vote
1 answer
300 views

Optimising returns weighted by Sharpe ratio in the context of Supervised Learning

In the Kaggle Jane Street market prediction competition we are put in a Supervised Learning Framework to deal with 'trade opportunities'. That is, we are given instances of previous trade ...
Lucas Morin's user avatar
1 vote
0 answers
81 views

$\epsilon$-arbitrage model

In the model here described, Bertsimas says that we can use the Robust Optimization to find the replicating portfolio the value of which is such that minimize the difference $|P(\widetilde{S},K)-W_T|=\...
Marco Pittella's user avatar
1 vote
0 answers
175 views

There are several ways optimize portfolio, why use Black Litterman rather than Mean variance

I know there are two ways to optimize portfolio. What are the limitations and advantages by using Black Litterman over Mean variance.
Guifan Li's user avatar
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1 vote
0 answers
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Maximizing sharpe ratio using cvxpy or cvxopt

I have a dataframe $n$ by $m$ representing $m$ timeseries of returns (each column is a different time series) with total $n$ number of observations, I want to find weight vector of length $m$ such ...
qwer's user avatar
  • 333
1 vote
0 answers
148 views

CVaR portfolio optimization with risk aversion parameter

I'm trying to implement the Rockafellar's function described in this paper http://past.rinfinance.com/agenda/2009/yollin_slides.pdf with a risk aversion parameter for my thesis. The function to ...
Malva's user avatar
  • 11
1 vote
0 answers
270 views

Error in optimize.portfolio with transaction costs constraint

I am experimenting with the PortfolioAnalytics package to optimize portfolio with dollar neutral and transaction costs as constraints to the quadratic utility objective function. A sample R snippet is ...
aptportfolio's user avatar
1 vote
0 answers
158 views

PortfolioAnalytics: Training window based on entire history before rebalancing in 'optimize.portfolio.rebalancing'?

I am fairly new to PortfolioAnalytics and R in general. I am trying to do some backtesting of a minimum variance portfolio. I have weekly, monthly, quarterly and yearly return data of 3 selected ...
LarLee8's user avatar
  • 11
1 vote
0 answers
267 views

Minimizing Correlation to Index

In his PhD thesis in the chapter Market Neutral Portfolios, page 69, [1] Valle sets up an optimization problem which minimizes the absolute correlation of the portfolio log returns to the log returns ...
Hans-Peter Schrei's user avatar
1 vote
0 answers
92 views

How to choose trades over time when capital is limited

Say I'm in the business of trading forward contracts. So at some point in time, I look at the markets, and determine a number of trades I could make. For each trade, I know the profit I expect to make,...
ggambetta's user avatar
  • 111
1 vote
0 answers
73 views

Generate P Value from stationary bootstrap following Politis & Romano (1994)

For my master thesis I am analyzing the performance of trading strategies. For this I need to avoid data snooping by utilising the FDR approach. I follow closely the procedure presented by Bajgrowicz &...
Pavlov's user avatar
  • 11
1 vote
0 answers
39 views

Dynamic counterpart for model tunneling/optimization using past data

When we tune a model to optimize parameters for a strategy using past data, even if controlling for overfitting (checking out of sample performance) and refreshing the analysis from time to time, we ...
LuaLua's user avatar
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