# 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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### 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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### 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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### 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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### How to backtest a sample of trades to optimize stop loss on losing trades and profit targets on winning trades?

I have a history of hundreds of executed trades. Given those trades, I want to know if there's a tool or framework that can help me figuring out: What would have been the most cost efficient stop ...
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### 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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### 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 ...
247 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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### 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 ...
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### 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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### 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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### 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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### 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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### 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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### Constraints for a Long-Short Mean Variance Objective Function

Problem: I am trying to set up constraints for a long/short mean variance optimization problem. My constraints include: beta neutrality cash neutrality equality constraints on categories: <...
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### 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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### 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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### 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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### 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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### Compute tangency portfolio with asset allocation constraints

I am looking to compute the tangency portfolio of the efficient frontier, but taking into account min_allocations and ...
183 views

### Question about quadratic form of f* in the Continuous Kelly Criterion

I am trying to follow the Optimal Kelly derivation on Wikipedia for two continuous assets: one risky and one risk-free. The derivation begins by assuming that the risky assets follows a GBM (a ...
138 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 ...
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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 proportional-integral-derivative ...
183 views

### Minimizing Correlation to Index

In his PhD thesis in the chapter Market Neutral Portfolios, page 69,  Valle sets up an optimization problem which minimizes the absolute correlation of the portfolio log returns to the log returns ...
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### Sequential Optimization

I am looking for the name of a sequential optimization, if that technique makes indeed any sense and exists. Given the solution $x^*$ to a non-linear non-convex problem \begin{equation*} \begin{...
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### Struggling with tau in Black-Litterman

According to the omega formula in B-L tau is used in the Omega estimation to determine the degree of uncertainty given to views of the investor: So, if tau is given a low value then the inverse of ...
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### How to minimize $CVaR_{\alpha}(\min(X,d))$, where $X$ is a random variable and d is the decision variable?

How to solve the following problem, $$\min_{d \in \mathbb{R}^{+}} \text{CVaR}_{\alpha}(\min(X,d))$$, where, X is a random variable whose distribution function $f_{X}(x)$ is given and $d$ is the ...
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### Market Making Strategies Found by Hamilton-Jacobi-Bellman Equation

Im working my way through the book "Algorithmic and High-Frequency Trading" (AHFT) by Cartea, Jaimungal and Penalva and i'm curious to see how the market making model with an exponential utility ...
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### Implementing the Sharpe's return-based style analysis on Python

I am trying to implement the Sharpe's return-based style analysis on Python. The problem is formulated as follows: ...
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### 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,...
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### Optimal portfolio construction for tactical asset allocation

This is the first time I post question here so if there is anything that does not follow the rule, please bear with me and let me know. I am trying to solve this optimization question but I don't ...
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### R: optimize timeseries to minimize “integral”

What I am looking to do is: for a given time-series $P_t$ (which will be constructed from different timeseries itself): $P_t$ = $\beta_1$$I_t^1+\beta_2$$I_t^2$+$\beta_3$$I_t^3$ $\qquad$ ($I_t^i$ ...
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### Optimal number of nodes for binomial lattice?

Let's suppose one is valuing a Euro call on a ZCB in a Black-Derman-Toy lattice. How many nodes/levels of discretization are optimal? Obviously too many creates computational issues and too few ...
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### maximize Sharpe ratio in portfolio optimization

I am trying to understand how to maximize Sharpe ratio in portfolio optimization. \boxed{\begin{align}\max\>&\frac{r^Tx-r_f}{\sqrt{x^TQx}}\\ & \sum_i x_i = 1\\ & x_i\ge 0\end{align}} ...
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### Javascript calculating IRR using Newton method

I leveraged the github code (https://gist.github.com/ghalimi/4591338) to compute IRR using Newton method. When I replicated the codes step by step in excel, I'm able to find the optimized resultRate ...