# 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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### 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 ...
137 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. ...
415 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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### 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 ...
215 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 ...
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### 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 ...
194 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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### Why is Markowitz portfolio optimisation so popular considering it is worse than an equal weighted portfolio?

The original paper by Markowitz from the '60s has ~20,000 citations (definitely popular). However several papers I came across show that a $\frac{1}{n}$ asset allocation gives higher Sharpe ratios (...