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 could I solve the following optimization problem?
Suppose that $(\Omega,\mathcal{F},\mathbb{P})$ is a standard probability space and $Z_t=(Z_t^1,Z_t^2)$ is a two dimensional Brownian motion with the filtration $\mathcal{F}^Z_{t}$ and $Z_t^1$, $Z_t^2$ ...
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Optimal leverage for strategy with normal returns
Given a strategy with normal returns with mean 5% and standard deviation 10% what is the optimal leverage (up to a maximum of 2x) to maximize the expected wealth? With the same setting, if trading is ...
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Transform non-linear HJB PDE into system of linear ODEs [closed]
I am reading this market making paper, and am trying to understand the transformation presented on page 6. A good resource for background relevant to the transformation is this other market-making ...
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PortfolioAnalytics: Out-of-sample optimization with transaction cost constraint using ROI solver does not work
I am currently trying to run an out-of-sample-optimization with the PortfolioAnalytics package in R, where the quadratic utility function of the investor also penalizes transaction costs (80bps) ...
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Calibration for CIR Model Discretization for Predictor Corrector and Milstein method
I'm new to Quantitative Finance. I've data which I need to fit a CIR model and estimate its parameters.
$ dX_{t+1} = a(b-X_{t})dt + \sigma \sqrt{X_t}dW_{t} $
While I can fit and obtain ...
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Is "extreme CVaR" (CVaR from extreme value theory) elicitable or conditionally elicitable with some other statistical mapping (like VaR)? [closed]
I am not able to find loss function (scoring function) extreme CVaR (CVaR from extreme value theory) which is a conditionally elicitable statistical mapping (conditioned on VaR).
In this regard, can ...
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What is the meaning of the following mathematical equations? [closed]
Let's say that we have a discrete probability distribution, where
$$ x_i $$ represents each of the possible outcomes (discrete set of possible outcomes), and
$$ L $$ represents the expected value we ...
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How to use simplex method for initial estimates of parameters in Nelson-Siegel-Svensson
I came across a BIS note about the estimation of the Nelson-Siegel-Svensson method. Currently, I'm trying to implement this. However, one step is not fully clear to me. Let me outline the steps of the ...
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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 ...
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Binomial Tree for CDF
I'm tasked with solving an optimal stopping problem relating to stochastic process representing a firms profit namely $X_t = X_0 + \mu t + \sigma Wt$ where $X_0, \mu$ and $\sigma$ are constants.
...
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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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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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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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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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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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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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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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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),
$$
which considers the co-skewness ($M_3$ tensor), $γ$ is the ...
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Is quadratic programming used to maximize portfolio skewness and kurtosis?
Quadratic programming, a type of convex optimization, is used to solve the minimum variance portfolio weights $$w = \arg \min_w \sigma_P^2 = w^\top \Sigma w$$
because the objective function coincides ...
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Linear programming optimization problems in finance
I'd like to know what are, if any, the applications of linear/non linear programming optimization techniques for financial markets.
I'm a business major, and I want to find an argument for my thesis ...
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Maximize account equity over a historic time series
Inputs:
array of OHLC forex bars of size N, max leverage L, e.g. 200:1, a fixed bid ask spread S, a fixed lookahead whipsaw window W (e.g. 3 bars long, see below).
Desired output:
a list of tuples {...
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Double objective in portfolio optimization
Is there anything infeasible or ethically wrong about optimizing portfolios like this?
$$\min_w \enspace w' \Sigma w + w' C w$$
where $\Sigma$ is the asset return covariance matrix, and $C$ is the ...
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Configuration of control parameters tol and delta in the rsolnp package
I am working with the rugarch package which includes a solver.control argument. I am using the solnp solver. I can pass values for tol and delta. In the rsolnp the authors suggest that the control ...
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Optimizing Portfolio Return by Targeting Variance
I understand Markowitz and targeting returns to minimize our variance. I know this optimization problem well and its constraints. However when the reverse scenario is to be considered I get very ...
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How to optimize a non-linear least squares problem with cvxpy/cvxopt
I know how to minimize a linear function $f : \mathbb{R}^{n} \rightarrow \mathbb{R}$ with CVXPY but in my problem the function $f$ is quadratic and hence the problem is now in the form :
$$\lVert AW-...
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