# Tagged Questions

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.

238 views

### Constant Relative Risk Aversion

The question: Consider a person with constant relative risk aversion p. (a) Suppose the person has wealth of 100,000 and faces a gamble in which he wins or loses x with equal probabilities. ...
44 views

### Multi-objective optimization: Where to find qualified examples for portfolio management?

I am looking for qualified examples of multi-objective optimization applied to a portfolio management situation in non-normal markets. Where can I find one or more examples of such a multi-objective ...
127 views

### Asset Liability Management Test Topic Interpretation

I will write a test based on Excel and one of the topics is "The Asset Liability related analysis: including the input assumptions generation, constraints, portfolio optimization analysis and results ...
186 views

### Portfolio Optimization to include ALL Securities?

I'm currently optimizing portfolio weights for an investment team with N stocks. We buy stocks with a conviction it will generate a return and it is up to me to determine weighting. However, with ...
110 views

73 views

### Transform MPT optimization problem

I am trying to teach myself about MPT and optimization. I understand that MPT solutions can be found using three equivalent optimization problems: Minimizing variance for given return limit ...
136 views

### What are the roles of “Game theory” and “optimisation (linear, integer, conic)” in Finance, Mathematical Finance? [closed]

Would you please give me some information about application of "Game theory" and "Optimisation" in Finance and Mathematical Finance? which is more important to know and learn? How about "multi-...
272 views

I am using MATLAB to do an optimisation. The QP minimisation problem is set up in the standard form shown below. The optimisation is used to calculate the weights (x vector in the equation below) of a ...
202 views

### Efficient Frontier Derivation: why minimize half the portfolio variance instead of just the variance?

In Robert Merton's derivation of the efficient frontier of a portfolio, he minimizes $\frac{1}{2}\sigma^2$ over the investment weights in each asset, where $\sigma^2$ represents portfolio variance. ...
81 views

### optimisation problem with linear constraint

I have an optimisation problem. I wish to maximise a function subject to a constraint. It is the constraint that is causing me problems. I am using an addin in Matlab which does the optimisation ...
380 views

### How to combine Gaussian marginals with Gaussian copula to obtain multivariate normals?

in the book "Numerical Methods and Optimization in Finance" I red the following: "Combining the Gaussian copula with Gaussian marginal gives a fancy way of expressing multivariate normals. However, ...
20 views

### Standard errors clustered along the time dimension in pooled panel logit model

I'm trying to estimate a logit model on pooled panel data set (unit of observation is firm-year). My dependant variable is default indicator and I have several macro variables as independant variables....
60 views

### What do “Exposure Bounds” mean in Portfolio Optimization?

I've just started reading up on Portfolio Optimization models and have come across the use of exposure bounds to mitigate the sensitivity of the optimized model solution, owing to parameter estimation ...
122 views

### State Space models with Short Time Series

My problem is that I have a state space model that I estimate using the Berndtâ€“Hallâ€“Hallâ€“Hausman (BHHH) algorithm. The state space model is relatively simple in that the hidden part follows a pure AR(...
278 views

### Which is the better risk sensitive measure?

Consider the two following optimization problem 1) $$\min_{\theta} \ln E_{\theta}[ e^{X}]$$ 2) $$\min_{\theta} E_{\theta}[ X]$$ with the constraint $$Var_{\theta}[X] <c$$ Is it true that ...
38 views

### Doubt on risk cost criterion

I want to minimize some kind of risk sensitive cost. But, I am confused what cost criterion should I use. I am aware of only expected exponential utility. I want to know what are the other such ...
495 views

### multiperiod optimization using R

I'm interested in multistage optimization problems. Are there any good R packages around to solve such problems over time? I'm not at all an expert in it, so maybe someone knows a good paper / lecture ...
83 views

### Max Likelihood via Marquardt Optimisation

I asked a related question here: How to apply Levenberg Marquardt to Max Likelihood Estimation I tried the approach suggested it works for some of the parameters but not the variances. I spoke to ...
69 views

### robust regions in grid search

I have a strategy f that takes parameters x,y (for x,y taking values in integer ranges). I get two grids (of returns and volatility values) from computing f(xi,yi) for integer ranges x1 <= xi <= ...
135 views

### Combining BHHH and Levenberg Marquardt

I already asked a question related to this here: How to apply Levenberg Marquardt to Max Likelihood Estimation I know understand how Levenberg Marquardt (LM) can be applied to the objective function....
316 views

### How to apply Levenberg Marquardt to Max Likelihood Estimation

In this paper on p315: http://www.ssc.upenn.edu/~fdiebold/papers/paper55/DRAfinal.pdf They explain that they use Levenberg Marquardt (LM) (along with BHHH) to maximize the likelihood. However as I ...
1k views

### Do hedge fund trading desks use portfolio optimization?

I tend to think that hedge funds that actively trade (and most of the ones I have seen trade very actively), don't use optimization methods like MVO or ...
178 views

### Blackâ€“Karasinski - Market Price of Risk

In the past I have calibrated simple short rate models to the term structure by using maximum likelihood to get the parameters of the Vasicek/CIR sde, and then use the ZCB formula and the current ...
315 views

Let's say we have a stock which our only actions are buy, sell and hold (with or without shorting). If we have sufficient past data of the stock, how can you determine the optimal trading action ...
1k views

### How do I do a mean variance optimization with constraints?

I am using python and the cvxopt library to calculate an efficient frontier, per the docs: http://cvxopt.org/examples/book/portfolio.html However, I cannot figure out how to add a constraint so that ...
531 views

### Mean-variance portfolio & quadratic programming

I am somewhat confused when it comes to modern portfolio theory, mean-variance portfolio optimization and its quadratic programming formulation. Issue 1: Formulation of mean-variance portfolio ...
45 views

### How do I determine what is a separate objective in a multi-objective portfolio optimization?

Is there a general rule to determining when to separate objectives when developing a multi-objective portfolio optimization? For example, one might start with a standard portfolio optimization of ...
37 views

### Approaches to check/validate the output of an optimization algorithm

Let's say we want to optimize the a function $f(x_1,\dots, x_n)$ with $(x_1, \dots , x_n) \in \mathbb{D}^n$. For the sake of simplicity let $\mathbb{D}^n$ be the unit sphere. We chose an optimization ...
216 views

### Is there any academic material regarding robust optimization with fixed transaction costs?

I'm looking to piece together a robust optimization model that handles robust optimization with fixed transaction costs and other combinatorial variables (e.g. asset count constraints). Here's what I'...
247 views

### What R-packages for SOCP problems are there?

Currently, I am looking deeper into the topic of second-order cone programming. Could you suggest packages that solve SOCP-problems in R? With your answer, please provide a short description of ...
148 views

### A doubt about Evans and Jovanovic (1989) economic model for entrepreneurs with credit constraints

[I already posted this question on the math forum of stackexchange and I was advised that I should post this question here] In Evans and Jovanovic (1989) you will find a model for entrepreneurs with ...
452 views

### Optimizing Principal Component factor weightings over time

I was given the returns of a cross-asset class portfolio of ETFs and I conducted PCA to obtain factors on dates from T-n, T-3, T-2,..., T. What I would like to do is decompose the market moves from T+...
327 views

### Optimization: Factor model versus asset-by-asset model

In portfolio management one often has to solve problems of the quadratic form $$w^T \Sigma w + w^T c \rightarrow Min$$ with portfolio weights $w \in \mathbb{R}^N$ a constant $c \in \mathbb{R}^N$ and ...
411 views

### Portfolios from Sorts

Some time ago Almgren and Chriss proposed a method for portfolio optimization based on sorting criteria such as $r_1 > r_2 >... > r_N$ instead of explicit expected returns: see portfolios ...
560 views

### Optimal trading strategy in toy world of simple Hidden Markov model with Gaussians

I want to solve the following optimization problem: What is the optimal general trading strategy (in the sense of the highest Sharpe ratio) on a time series which is the result of a Hidden Markov ...
The quadratic optimization (min variance) $$w^{T} \Sigma w \rightarrow \text{min},$$ where $w$ is the vector of portfolio weights and $\Sigma$ is the covariance matrix of asset returns, is a well ...