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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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1 vote
0 answers
27 views

Implicit function theorem and sensitivities to market risk for Nelson-Siegel-Svensson model

I’m calibrating the Nelson-Siegel-Svensson model to market rates and I’m trying to compute the sensitivities of the NSS parameters to those said rates: $$r\left(T\right)=\beta_{0}+\beta_{1}{\frac{\...
2 votes
1 answer
86 views

Proof of weights maximizing sharpe of a portfolio

Given a portfolio of $n$ assets with mean vector $\mu$ and correlation matrix $\Sigma$, the optimal weights $w$ on the $n$ assets to maximize overall sharpe is found by $$\max_{w:||w||=1}{\dfrac{\mu^T ...
0 votes
1 answer
34 views

How do I reformulate this max GMV ratio constraint in convex way?

Assuming I have N stocks. I want to have the following constraint in my optimization problem setup. $|x_i| \le \alpha \sum_{j}^N |x_j|$ where $\alpha$ is known, say 0.6. The intuition here is the GMV ...
4 votes
2 answers
239 views

A quant job interview question about (toy) futures

On Monday, you receive prices for each day of the week: $X_{1,1}, \ldots, X_{1,5}$. On Tuesday, you receive prices for Tuesday, Wednesday, Thursday, and Friday: $X_{2,2}, \ldots, X_{2,5}$. On ...
3 votes
1 answer
606 views

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 PID controllers for these applications?
1 vote
2 answers
81 views

Reverse Optimization: finding the returns that satisfy specific weights given one known return

Here is the premise: I have a three asset portfolio, I know the assets covariance, the client's risk aversion and the expected return of one of the assets. I also have a desired set of weights. So, 1) ...
1 vote
1 answer
300 views

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 ...
-3 votes
1 answer
103 views

sharpe ratio, convert into convex function, not understand that constraint, [duplicate]

I am reading about tranforming sharpe ratio into convex problem After some following, its converted into min xTxy s.t. (u-rf e)x = 1 ...
0 votes
0 answers
43 views

GARCH for Mean Variance Optimization

I am currently trying to carry out a mean variance optimisation, with the implementation of GARCH. I'm not sure if this is going to make complete sense as my understanding of GARCH is limited. In the ...
0 votes
0 answers
53 views

Robust or Stochastic Optimization Approach for Maximizing Profit with Limited Price Information

I am tackling a linear maximization problem where I need to select the optimal product among several options over a series of weeks, given certain constraints, in order to maximize future profit. The ...
0 votes
0 answers
91 views

Using regression to find optimal parameters for a trading strategy based on market regime

I am still fairly new to the field so forgive me if the whole post and my questions sound stupid. A bit of explanation first. So i have a trading strategy which is an extension of an Avellaneda-...
1 vote
0 answers
53 views

Am I overcomplicating this approach to optimal actions based on a forecast?

I have been attempting to implement a simplified version of the model used in this paper which, given a forecast of future data, provides an optimal way of acting on it by choosing an optimal sequence ...
0 votes
0 answers
31 views

Pricing FRA rates from changes in rates due to ECB meetings and vice versa

This is somewhat building on top of my last question: Explicit step by step curve construction using FRAs I'm trying build (in python) and understand something that will allow me to reprice 6M EURIBOR ...
1 vote
0 answers
33 views

Duality in conic quadratic programming for good deal measure

I am working on a problem relating to what is known as the "Good Deal risk measure" for production valuation in incomplete markets. I have created the following primal optimization problem, ...
0 votes
1 answer
109 views

Why not inequality constraint in mean-variance portfolio optimization?

Question 1: In Modern Portfolio Theory, the case where we minimize variance given a set return and that the weights sum to 1, why is the return set as an equality constraint, not an inequality? ...
0 votes
0 answers
34 views

Analytical solution to short-sale constrained portfolio

Say that we want to find the efficient mean-variance portfolio (i.e. minimize variance given that weights sum to 1 and given a set target return) and impose a short sale constraint such that $w_i \geq ...
5 votes
3 answers
3k views

How can I find the portfolio with maximum Sharpe Ratio - Using Lagrange Multipliers

In Markowitz' portfolio theory we can construct portfolios with the minimum variance for a given expected return (or vice versa). Across expected risks, this traces out the well-known efficient ...
0 votes
0 answers
31 views

Minimizing tracking error for a 150 / 50 portfolio against the S&P500

I am trying to minimize tracking error ex-ante for a 150 / 50 portfolio, eg. it is 150 units long, 50 units short and market exposure of 100 units. It uses all 500 stock in the S&P500. I've ...
14 votes
5 answers
1k views

Quantum Computing for Quantitative Finance

It's been a while that quantum computing is looked as the next step in computational science. I somewhat always tought we were decade aways from it's happening but it appears I was wrong: ibm-quantum-...
3 votes
1 answer
198 views

Dealing with Inventory Risk

I am reading a paper$^\color{magenta}{\dagger}$ on market-making and having trouble understanding a point. Towards the end of section 2, the authors stated that: $$\sup_{(\delta_t^a)_t, (\delta_t^b)_t ...
0 votes
1 answer
243 views

Wrt speed, how optimised is QuantLib's Heston pricing class?

I have a pricing formula that is 300x the speed of the QuantLib's Heston pricing class. Is it incredibly slow? For context, on a slow 1.6 GHz Dual-Core Intel Core i5 processor, my method can reliably ...
0 votes
0 answers
149 views

Constraints in a Mean-Variance Optimization Case

Might be a repeat question, feel free to close if it is. I am trying to perform a mean-variance optimization (maximizing the Sharpe ratio) for lets say 5 assets. Besides the weights of the assets ...
0 votes
0 answers
61 views

Adjusting the p-value of a strategy for number of parameters

Let's say I have some metric and I'm trying to evaluate whether it's predictive with respect to returns. I plan to only take trades where the value of the metric is above a certain threshold, such ...
0 votes
1 answer
175 views

Calibrating the Heston with the Levenberg-Marquardt algorithm

I am trying to implement the Levenberg-Marquardt algorithm similarly to Cui et al. Full and fast calibration of the Heston stochastic volatility model, 2017 here (although using a different method to ...
1 vote
0 answers
203 views

Calibration of $\rho$ in the heston model

When calibrating the Heston model, the gradient of the price of the call/cost function wrt $\rho$ (correlation between $S$ and $V$), is a lot less than the other parameters like $v_0$ and $\bar{v}$. ...
3 votes
0 answers
309 views

Which C++ implementations of Levenberg-Marquardt does the "industry" use?

According to your various experience, is there an industry consensus about which C++ implementation of the Levenberg-Marquardt algorithm to use ? I came across two places where it was the C numerical ...
3 votes
1 answer
473 views

Optimal Fitting Criteria of SABR

I was reading about SABR Model and curious about this. The process of fitting the SABR model involves finding values for the parameters α, β, ρ, ν that minimize the difference between model-implied ...
2 votes
1 answer
550 views

PortfolioAnalytics [R] - optimize.portfolio.rebalancing / rebalancing period

I am having difficulties trying to set up the rebalancing period to semi-annual or every 9 months in the optimize.portfolio.rebalancing function in the package ...
3 votes
2 answers
2k views

Dmat argument in solve.QP R function: Cov or 2*Cov?

Background My final objective is to find a portfolio located on the efficient frontier from a choice of 100 stocks from a stock index (eg. S&P500). This efficient portfolio will be such that ...
1 vote
0 answers
89 views

Optimal portfolio as combination of target and minimum tracking error portfolios?

Dear Quant StackExchange I seek some intuition for how my portfolio behaves given constraints. In a universe of say 5 assets, I have a "target portfolio" with weights that are found from ...
4 votes
1 answer
2k views

Parameters in Nelson-Siegel model and Nelson-Siegel-Svensson model

I am trying to determine the parameters for the Nelson Siegel and Nelson Siegel Svensson model and try to solve SE=$\sum_{i=1}^{n_{i}}(y_{t_{i}}-\hat{y}_{t_{i}}(X))^{2}$ where $y_{t_{i}}$ denotes the ...
1 vote
1 answer
430 views

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: ...
5 votes
1 answer
687 views

How to (efficiently) calculate the maximum possible return of a perfect "crystal ball" investment strategy?

I am new to the world of investing, so please excuse the clumsy wording of the question... there is probably a better term for what I am looking for or maybe this is even a known/classic problem. If ...
2 votes
1 answer
276 views

How do your solve for trader's optimal demand in market similar to Kyle's model?

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 $Z_t^1$, $Z_t^2$ ...
1 vote
1 answer
155 views

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 ...
9 votes
4 answers
15k views

Why do we assume quadratic utility in portfolio theory?

In my text (Investments by BKM), the investor's mean-variance utility (given as $U = E[R] - \frac12A\sigma^2$) is stated to be the objective function we wish to maximize. Upon further digging, it ...
1 vote
0 answers
66 views

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 ...
4 votes
3 answers
4k views

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?
2 votes
1 answer
300 views

Numerical Optimizer Matlab Calibration LMM

I am trying to mimimize the following function in order to calibrate the Libor Market Model $$\sum_{i=1}^{n} \left(\sigma_i^{market}-\sigma_i^{Reb}\left(a,b,c,d,\beta\right)/\sqrt{T_i}\right)^2,$$ ...
0 votes
0 answers
122 views

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 ...
1 vote
0 answers
34 views

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 ...
0 votes
1 answer
69 views

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 ...
2 votes
0 answers
129 views

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 ...
0 votes
2 answers
282 views

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 ...
1 vote
2 answers
299 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$ ...
0 votes
0 answers
60 views

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. ...
68 votes
9 answers
92k views

What are some useful approximations to the Black-Scholes formula?

Let the Black-Scholes formula be defined as the function $f(S, X, T, r, v)$. I'm curious about functions that are computationally simpler than the Black-Scholes that yields results that approximate $...
3 votes
1 answer
469 views

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 ...
0 votes
0 answers
64 views

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,...
1 vote
1 answer
45 views

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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