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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64 views

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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57 views

Linear programming related to finance

I'd like to know what are, if any, the applications of linear/non linear programming optimization techniques for financial market. I'm a business major, and I want to find an argument for my thesis ...
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148 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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86 views

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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15 views

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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36 views

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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30 views

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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58 views

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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1answer
41 views

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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106 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}...
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46 views

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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114 views

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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36 views

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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67 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 ...
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1answer
64 views

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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1answer
22 views

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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2answers
132 views

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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1answer
164 views

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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47 views

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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1answer
185 views

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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1answer
28 views

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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31 views

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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71 views

Is optimising for the Final Wealth is the same as optimising log of growth rate in Kelly Criterion?

A direct, brute force approach could be used to find the Optimal Portfolio. Consider simple play. There's a biased coin with 55% probability of win. The simulator play as a single person with 100$ ...
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1answer
192 views

Optimization with turnover constraint

I am optimizing using scipy.optimize using SLSQP. I am looking to minimize the variance with some upper bounds and lower bounds on each stock. I am also looking to constraint the weight so that the ...
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84 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 ...
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1answer
415 views

solve.QP error: constraints are inconsistent, no solution!

I am trying to solve a constrained optimization with the following statement and struggling with the error constraints are inconsistent, no solution!: ...
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63 views

Spread option static replication

I have a methodology for hedging a spread option but not sure if it makes any sense, or if I can do any better. Happy to hear your advice! Suppose you have a spread option paying off $P_T(r_T,s_T)=(...
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1answer
97 views

Choosing best expressions from all possible combinations on variables, unary operators and binary operators along with hyper parameters

I have a few financial variables of a stock universe like OHLC prices, volume, and other fundamentals with varying time-frequency. Using this set I'm creating an expression that gives the weights to ...
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70 views

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,...
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49 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 ...
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41 views

Tangency portfolio with two additional constraints

I know that the formula for determining the weights of the Tangency portfolio is given as $w_{tan}$ = $\frac{\Sigma \mu}{\iota^{\prime}\Sigma\mu }$, but I was wondering how to derive the weights in ...
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1answer
224 views

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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2answers
411 views

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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29 views

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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1answer
69 views

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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2answers
468 views

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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2answers
578 views

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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2answers
1k views

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 ...
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1answer
167 views

Which Maximum Diversification Approach in MATLAB is correct?

I am currently trying to find the portfolio weights of the Maximum Diversification Portfolio and found two approaches which result in different outcomes. The first one is based on this paper:https://...
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1answer
76 views

Achieving desired fx exposure with using minimum pairs possible

Let say my algorithm tells me to get the following positions through opening fx positions: CUR NET POSITIONS GBP 236.96379 USD -310.58000 CHF 0.02000 There are 2 ways to achieve this: Long ...
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1answer
141 views

Mean-variance maximization

I denote by $W_0$ and $W_1$ the wealth of an investor at $t=0$ and $t=1$, respectively. Let $r_f$ be the risk free rate, $r$ the vector of returns of the risky assets in excess of the risk free rate, ...
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1answer
107 views

Monte Carlo computational cost

Hello. I'm reading the above paper and I do not understand how they managed to solve eq (17.35) -- i've seen many papers skip through this as trivial and didn't bother to show the method to get there. ...
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1answer
54 views

How to optimize a series of equations whose outputs are a variable of the subsequent equatinos

The basic question is, given $f(x) = y$ and $f(y) = z$, how can you find $x$ such that $z$ is at its maximum? I can optimize each equation independently, but I do not know how to optimize when ...
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1answer
134 views

Which data provider do you recommend? [duplicate]

i need to run optimization models and backtests on developed market equities. I have access to Refinitivs Eikon, but it doesnt have a backtest tool and downloading the data is a challenge on his own. ...
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2answers
369 views

Estimation of Risk-Neutral Densities Using Positive Convolution Approximation - Python

I'm trying to estimate the risk-neutral density through positive convolution approximation (introduced by Bondarenko 2002: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=375781). I'm currently ...
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3answers
3k views

Maximum Sharpe portfolio (no short selling restrictions)

Suppose we have $n$ assets whose expected return vector is $r$ and is positive, and whose covariance matrix is $\Sigma$. Is there a closed form or quasi closed form (like the eigenvector of a matrix ...
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2answers
145 views

Do you optimise models on bootstrapped time series?

As Quants, we soon learn to optimise models, by fitting them to historical time series, e.g. the historical daily returns of some stock. But the historical series of daily returns is just one ...
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0answers
77 views

Dealing with Inventory Risk - Paper

I am reading the paper - Dealing with Inventory Risk and I am having trouble understanding a point made in the paper. The author(s) say towards the end of section 2 that: and says that: $ \mathcal A ...
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1answer
172 views

Market Portfolio Optimization

Consider the minimization problem $$\min\left\{\frac{1}{2}x^T\Sigma x - \lambda(\mu-r_f)^Tx\right\}$$ and assume the CAPM model, i.e. $$r_i-r_f = \beta_i(r_m-r_f) + \varepsilon_i$$ Assuming $\...

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