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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23 views

Stochastic control (HJB) for wealth process involving stopping times

Given a wealth process that evolves as $$d w_t = r w_t dt + \theta_t ( \sigma dW_t + (\mu-r) dt) - c_t dt.$$ where $\theta_t$ is the worth of holding at time $t$ and $c_t$ is the consumption stream. ...
2
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1answer
43 views

Markowitz Mean-Variance Implied Returns

What is the closed form solution for the following inverse Markowitz problem? Given a mean-variance optimized fully invested portfolio $X$, a risk aversion parameter $\lambda$ and a var-covar ...
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0answers
20 views

Calculating the optimal portfolio for an investor with quadratic utility

The problem is from Asset Pricing and Portfolio Theory by Back and can be found here. The relevant info from section 2.5 can be found here. Given that we have the Expected value and the variance of ...
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1answer
53 views

constrained portfolio optimization by fmincon

I am working through this paper, http://www.nber.org/papers/w8922.pdf I want to implement the portfolio weight constraints see page 6-7. Here is the brief overview of my problem: Let ...
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1answer
54 views

constrained portfolio optimization in matlab

I am working through this paper, http://www.nber.org/papers/w8922.pdf I want to implement the portfolio weight constraints see page 6-7. Here is the brief overview of my problem: Let ...
2
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0answers
66 views

Portfolio choice problem of a CARA investor with n risky assets

Ok, I am working on a problem that consists of the following: I am looking to solve the portfolio choice optimization problem (maximizing utility with a known utility function) in the case where all ...
2
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1answer
108 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. ...
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0answers
24 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 ...
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1answer
34 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 ...
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2answers
133 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 ...
2
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1answer
50 views

Maximizing utility subject to a wealth constraint

Let $\tilde{E}$ be the risk neutral expectation, and $X_t$ the wealth that time t and $R$ the return of a risk-free investment. Consider maximizing the function $EU(X_N)$ subject to ...
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13 views

dynamic programming with serially independent returns

Book suggests that "asset returns are assumed to be serially independent, so wealth is a single state connecting one period to the next". I understand path dependency is lost in case of serial ...
2
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1answer
88 views

formulating MVO with costs

I am trying to formulate this simple MVO utility function with a linear transaction cost penalty added using Quadprog in MATLAB tcost = 0.001; lambda = 4; mu = vector of expected returns (say 4x1) S ...
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50 views

Model-independent dynamic portfolio optimization techniques

For a problem where we need to optimize the portfolio based on the data, going for Markowitz MPT has the following advantage: we only have to estimate mean and covariance to find optimal weights. I'd ...
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1answer
67 views

Optimization metric that takes into account number of trades vs expectancy

In optimizing my automated trading system I find that certain combinations while increasing the expectancy: ...
2
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4answers
197 views

Portfolio Optimization using S&P Universes

Assuming a set portfolio optimization problem, if all optimization inputs are kept constant, what would you expect, in terms of results, if you run the same optimization using the S&P500 as ...
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224 views

Calculating the efficient frontier from expected returns and SD

I'm trying to calculate the efficient frontier (and the optimal portfolio at the Sharpe ratio) given two vectors for a portfolio: (1) expected returns and (2) historical standard deviations. I would ...
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2answers
55 views

Weighting with restrictions, but no clear objective function?

I have 40 shares in an index and I want to weight them based on their market value, define the known value as $x_i$ In the traditional way, the weight of each share is calculated as: $w_i = x_i / ...
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0answers
56 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 ...
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0answers
87 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 ...
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1answer
115 views

quadratic programming portfolio optimisation

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 ...
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1answer
102 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. ...
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1answer
70 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 ...
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2answers
97 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, ...
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0answers
17 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 ...
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1answer
56 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 ...
2
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0answers
88 views

State Space models with Short Time Series

My problem is that I have a state space model that I estimate using the Berndt–Hall–Hall–Hausman (BHHH) algorithm. The state space model is relatively simple in that the hidden part follows a pure ...
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1answer
171 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 ...
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33 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 ...
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3answers
265 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 ...
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0answers
67 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 ...
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0answers
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 <= ...
0
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1answer
58 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 ...
2
votes
1answer
140 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 ...
2
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3answers
257 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 ...
1
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1answer
135 views

Black–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 ...
3
votes
3answers
273 views

Determining optimal trading signals (buy/sell) from past data

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 ...
0
votes
1answer
427 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 ...
4
votes
1answer
279 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 ...
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0answers
42 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 ...
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0answers
50 views

Compute the average efficient frontiers with estimated parameters from generated time series

My overall objective is to analyse the impact of error in mean-variance analysis from historical data. I am given the returns and standard deviation for the five assets under consideration, as well as ...
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0answers
29 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 ...
2
votes
2answers
198 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 ...
2
votes
0answers
126 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 ...
2
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0answers
91 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 ...
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2answers
315 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 ...
4
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0answers
240 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 ...
7
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228 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 ...
5
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1answer
367 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 ...
5
votes
1answer
335 views

Min VaR and Min TE as second order cone program

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 ...