# 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 do i calculate the parameters a,b,ρ,m,σ for the SVI model? [closed]

How do i calculate the parameters a,b,ρ,m,σ for the SVI model using Python?
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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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### Conic programming for portfolio optimization instead of quadratic programming: Typo in source?

The benefit of using a cone constraint like $$\sqrt{\left(w^{2}+w^{2}\right)^{2}}<r$$ compared to a non-cone constraint like $$\sqrt{\left(w^{2}-w^{2}\right)^{2}}<r$$ is that the ...
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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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### Extreme and rare events affecting the market

There are extreme events affecting the high-probability [short-term] market such as lowering interest rates that rocket stock prices, even though such events are rare and the market's response can be ...
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### Martingale optimal transport

I'm a student and currently studying martingale optimal transport for deriving upper and lower contract bounds but i happen struggling on the fact that in most papers , interest rates are not taken in ...
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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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### Multiple tracking error constraints - is this problem convex?

Let's say I have a return forecast for each stock in the DAX index. I also have a covariance matrix for these 30 stocks. I want to solve for the 30 weights by maximising the forecast portfolio ...
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### Monte carlo error and minimum variance hedge ratio

So I was running a monte carlo simulation for two assets and a portfolio consisting of 1 quantity of the first asset and short a fraction x of the second asset to hedge, where the fraction is ...
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### 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 ...
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### Backtesting with a walkforward approach

I am setting up a backtesting using a walkforward optimization model to find out if a trading strategy performs well or not and I would like to clarify some doubts: First of all what is the correct ...
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### Suggestions for choosing an optimization algorithm for fitting custom GARCH models by QMLE in R?

I am trying to fit a custom GARCH model by QMLE in R. I have written out the log likelihood function and am now working on optimizing it. However, choosing an optimization algorithm has proven to be ...
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### Problem with the maximum likelihood for a GARCH-type of model

I'm currently working with the following GARCH process from Heston and Nandi (2000): \begin{align*} r_{t+1} - r_f &= \lambda h_{t+1} - \frac{h_{t+1}}{2} + \sqrt{h_{t+1}}z_{t+1} \\ h_{t+1} ...
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### Optimization problem with a constraint

Consider the following maximization problem \max_{\{\tau(\cdot),q(\cdot)\}}\int_{\underline{\theta}}^{\bar{\theta}}\left(\theta q(\theta)-\dfrac{\gamma\sigma^{2}}{2}q^2(\theta)-\tau(\theta)\right)f(\...
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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). ...
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### stochastic programming book recommendations

Hi: Can anyone recommend an introductory book on stochastic programming ? There are obviously so many books on Amazon but I can't tell easily which ones could be useful. It would be good if it had ...
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### Weighting function for parametric estimation of the Risk-neutral density function

I would like to estimate the Risk-neutral density function (RND) implicit in financial Call option prices by a parametric approach where the parameters of the RND (for instance mean and variance for a ...
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### setting up a inequality constraint that is dynamic

I have the following problem: typical mean variance minimize w_long(S)w_long.T + w_shortSw_short.T - lambda*mu I am having issue formulating this constraint in cvxopt lets say we have 10 securities ...
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### Why is it better to use evolutionary algorithms than OLS for solving index tracking problem?

I am currently using different optimization algorithms for finding constrained portfolio that best replicate choosen index. So i have a optimization task to minimize tracking error. I wonder why every ...
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### Optimization of Take-Profit and Stop-Loss

Three questions: What branch of mathematics would help me optimize profit if I have a trading strategy that on an individual trade basis (Trade 1, Trade 2, ..., Trade N) has a draw down of (X1,X2,......
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### How to modify EMSR when capacity for each fare class is different

In the normal EMSRa and EMSRb algorithms (EMSR= expected marginal seat revenue), each fare class is utilizes exactly 1 unit of capacity (for eg. one seat on a plane). But I have a similar problem for ...
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### Framework for hedging fx and utilizing correlation between asset returns

Can anyone point me in a direction (research paper, books, ..) which developes a framework/strategy for hedging currency exposure for an international bond portfolio? This paper finds optimal ...
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### Fixed Income Portfolio Optimization

I'm trying to solve for a maximum sharpe ratio portfolio in the fixed income space. To do so, i use CVXPY in python. I use this Paper as reference. This is my "setup": ...
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### How to calculate optimal portfolio using sector constraints in python

I'm looking into CVXPY at the moment. Main goal would be to be able to calculate the optimal portfolio, which in my opinion would mean that we need to maximise (expected return - risk free) / ...
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### Random Portfolios vs Efficient Frontier

I understand the concept of the efficient frontier and am able to calculate it in Python. But even when generating 50'000 random 10 asset portfolios, the single portfolios are not even close to the ...