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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How to understand this convex optimization method to find risk budget portfolio

Both the short course material coded by the CVXPY developers and an answer on Quant SE suggest that given a desired risk budget $b$, we can find the full-investment portfolio with weights $w$ that has ...
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how can I linearize a constraint of the form sum(min(x(i),y(i))) for a linear optimisation problem?

I have an linear optimisation problem with the objective : $ max PortfolioSpread(x_1,x_2,....x_N) = ∑_{i=0}^N(x_i*s_i)/budget$ s.t. $∑_{i=0}^N x_i = budget$ (+ other constraints) $∑_{i=0}^N min⁡(x_i,...
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Computing the highest vol for worst-of basket

I would like to ask a very general question. I am not expecting a closed-form solution to this problem so, any, help, idea or suggestion will be welcome. Suppose that we have a bunch of X stocks (10 ...
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Finding optimal option to maximise gains under given price hypothesis

Let's have Stock S at \$100 on January and my hypothesis is S will be trading at \$150 in July. Is there any Python/R package that I can feed with option prices from my broker and it would return the ...
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Nonlinear Constrained optimization for a CIR model

I want to calibrate a CIR model which is commonly used to model the evolution of interest rates. Briefly speaking, we know that its dynamics is of the form \begin{equation} dr_t = \kappa (\theta - r_t)...
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Why is the Sortino ratio non convex and also non concave?

I am considering as my objective the Sortino ratio: $\frac{\mu^{\top}x-R}{\sqrt{\mathbb{E}[(min\{0,(r-\mu)^{\top}x\})^2]}}$ In my textbook they state that this ratio just like the Sharpe ratio is ...
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How do you model optimal take-profit levels?

I have a very good model for directional trading. It gives me highly accurate predictions for short periods with predefined length (10 bars ahead; hourly timeframe). When I enter the trade I wait 10 ...
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Optimal Entry, Exit, And Stop Loss From Historical Stock Data

I'm trying to build a system that recommends stock trades. My goal is calculate optimal values for the following: Entry Parameter: expressed as a percentage change downwards from the opening price. ...
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linear optimization problem with non-linear constraint

I have the following optimisation problem which I want to solve using linear optimisation. Is there a way to represent the second constraint in a linear form in order to be able to use linear ...
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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 ...
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mean-variance optimization === max sharpe ratio portfolio?

Noobie here. I just wanna ask a simple question: in the context of portfolio optimization, is Mean-Variance optimization the same as the max sharpe ratio portfolio?
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How to solve an optimization problem with absolute constraint?

The optimization problem is shown below $$ \min_{\boldsymbol{w}}\boldsymbol{w}^T\boldsymbol{Sw}\\ s.t. |\boldsymbol{w}^T\boldsymbol{a}_i|>1, i=1,2,\cdots, n $$ , where $\boldsymbol{w}, \boldsymbol{...
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What is the definition of "cheapest collateral"?

Optimizing collateral is a hot topic in the financial industry. I came across the term cheapest collateral. What does it actually mean in the context of collateral optimization, please ?
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Portfolio optimization with Python/CVXPY: DCPError

I'm trying to implement a script for portfolio optimization on a sample universe of 3 future contracts. I have the following inputs: current allocation --> number of contracts currently held for ...
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Best optimization target for maximizing the odds of including the highest returning asset

I have an investment universe with several thousand assets that have different expected returns. All assets have the same expected volatility but different correlations to one another. Expected ...
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What are some tools to help optimize size of an ABS portfolio with many constraints?

What are some tools (python preferred) used in the ABS industry to optimize the size of a credit portfolio, given many constraints? Constraints can be things like Weighted Average Credit Metric (e.g. ...
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How to minimize Nelson-Siegel parametric form

Problem I am given the following function to minimize (w.r.t. $\theta$) $$f= \sum_{k=1}^5 \Big [ \sum_{i=1}^{N_k} CF_{k, i} \cdot e^{-r(t_{k, i}, \theta)\cdot t_{k, i}} - P_k^* \Big]^2$$ where $\...
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Multivariable objective function optimization similar to optimx in R

I have an optimization model in R that utilizes a single variable in my objective function. See below: ...
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Efficient frontier plot including Mean-Variance and Mean-CVaR frontiers

I am trying to compare the outcomes of a Mean-Variance and Mean-CVaR Optimization approach. I succeeded in plotting the efficient frontiers + tangency portfolios for both cases. Does anyone know how ...
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How to set a fixed return for mean-CVaR portfolio optimization?

I'm using the timeSeries and fportfolio package in R to minimize the CVaR with different constraints for a given portfolio. Everything is working out so far. However, I can't manage to set a fixed ...
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Optimisation Multiple Constraints - Using CVXOPT

I am trying to solve a linear algebra problem: an optimisation problem and I am using CVXOPT. I've split the problem into 3 components In its simplest form, The general formulation for CVXOPT is ...
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establishing an optimal take profit

Please let me know what you thoughts are on this. Say for example that you have a perpetuity, which guarantees you indefinite payments of a certain amount. Say then that you also have the opportunity ...
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Mixed-integer programming approach for index tracking

Suppose you currently own a portfolio of eight stocks. Using the Markowitz model, you computed the optimal mean/variance portfolio. The weights of these two portfolios are shown in the following table:...
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Minimize Composite Dispersion

Let's say that we have a composite of 10 fixed income portfolios, each with the same benchmark, the US Aggregate. Additionally, let's say that each portfolio has a position in Corporation ABC. The ...
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When looking for arbitrage among a LARGE amount of assets, is there an optimal way?

Looking for arbitrage opportunities when looking at 3 pairs of related currencies is easy. However if we assume that we have a large amount of currencies, is there an optimal way to swipe through them ...
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Curve fitting under different regions and stitching

Is there a way to fit a 2D curve under the following conditions: The curve is defined by 2 functions for x>a, and x<a Prefer a fit that is continuous and differentiable at x=a
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4 answers
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Cant replicate minimum variance portfolio variance by simulating many random portfolios in R

I have computed the theoretical minimum variance portfolio using the 30 stocks in the Dow. The formula used is: $$\underset{N\times 1}{\omega_{mvp}}=\frac{\lambda}{2}\cdot \Sigma^{-1}\iota=\frac{\...
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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 ...
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2 votes
1 answer
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Optimal Strategy in 3 Dice Game

In a recent interview I received the following question (an optimisation/strategy game)...which left me a bit stumped. The rules of play, you start with 0 points, then: Roll three fair six-sided dice;...
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Optimal withdrawal rate based on alpha and drawdown

My trading returns is about 50% monthly(alpha) and maximum drawdown is about 20%. Is there a mathematical way to define the optimal withdrawal rate X%(say when profit level reach y%) to avoid risk of ...
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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 ...
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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 ...
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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 ...
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Optimize Bollinger Bands Strategy

I was proving a very simple strategy with Bollinger Bands for a intraday timeframe (1 minute) that buy on lower band and sell in a higher band (Very common strategy), but in backtesting in E-Mini SP ...
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$\epsilon$-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|=\...
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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.
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Conic optimization in finance

Linear programming and quadratic programming are types of convex optimization that are often used. Does conic optimization or programming have any applications in finance? Or for where the previous ...
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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 ...
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Derivation of mean-variance portfolio weights as closed-form analytical solution from Lagrangean equations

I am trying to find a closed form solution for the constrained MVO problem below. $\max_w w'\mu - \frac{\lambda}{2}w'\Sigma w $ s.t. $w'$1 = 1 The Lagrange for the objective is $L(w, \gamma) = w'\mu ...
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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 ...
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1 answer
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Is quadratic programming used to maximize portfolio skewness and kurtosis?

Quadratic programming, a type of convex optimization, is used to solve the minimum variance portfolio weights $$w = \arg \min_w \sigma_P^2 = w^\top \Sigma w$$ because the objective function coincides ...
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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 ...
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1 vote
1 answer
159 views

Maximize account equity over a historic time series

Inputs: array of OHLC forex bars of size N, max leverage L, e.g. 200:1, a fixed bid ask spread S, a fixed lookahead whipsaw window W (e.g. 3 bars long, see below). Desired output: a list of tuples {...
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Double objective in portfolio optimization

Is there anything infeasible or ethically wrong about optimizing portfolios like this? $$\min_w \enspace w' \Sigma w + w' C w$$ where $\Sigma$ is the asset return covariance matrix, and $C$ is the ...
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Configuration of control parameters tol and delta in the rsolnp package

I am working with the rugarch package which includes a solver.control argument. I am using the solnp solver. I can pass values for tol and delta. In the rsolnp the authors suggest that the control ...
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Optimizing Portfolio Return by Targeting Variance

I understand Markowitz and targeting returns to minimize our variance. I know this optimization problem well and its constraints. However when the reverse scenario is to be considered I get very ...
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2 votes
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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-...
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-1 votes
1 answer
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How to build a portfolio following the Smart beta process by dividend? [closed]

I'm having trouble finding the method to track smart beta dividend management. I have an Excel file which contains the prices and the dividends of certain companies, and I want to build a portfolio ...
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2 votes
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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}...
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Dynamic programming and Bellman equation to obtain the maximum

This is the problem of Marhsall (1992) "Inflation and Asset Returns in a Monetary Economy" and Balvers and Huang (2009) "Money and the C-CAPM" Suppose an endowment economy where the representative ...
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