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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2
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3answers
82 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 ...
6
votes
1answer
117 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
votes
1answer
89 views

Starting values for constrOptim() in R

I want to perform a constraint optimization for Maximum Likelihood Estimation in R to forecast volatility of returns. The probleme is that my initial values aren't in the permitted region. Is there ...
1
vote
1answer
57 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-...
0
votes
1answer
64 views

Portfolio with a certain pay-off curve

I would like to find a relevant optimization option's portfolio models which can describe a certain pay-off curve (objective function) under same assumptions. For example, assumptions on how to limit ...
15
votes
0answers
3k views

Algorithm to fit AR(1)/GARCH(1,1) model of log-returns

I am fitting numerically an AR(1)/GARCH(1,1) process to index and stock log-returns, $r_t=\log(P_t/P_{t-1})$, where $P_t$ is the price at time $t$, and thus far am not clear on where the observed log ...
8
votes
0answers
205 views

Max option leverage strike

Since options represent leveraged stock investments, at which strike $K$ does a European option provide maximum leverage? Hereby define leverage $L$ as ratio of Delta/Optionprice: $$L(K)=\frac{\...
7
votes
0answers
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 ...
7
votes
0answers
798 views

Formula for the efficient portfolios (mean-variance optimisation)?

Consider the setting of mean-variance portfolio optimisation: $n$ assets with expected returns $\overline{r}_1,...,\overline{r}_n$ and standard deviations $\sigma_1,...\sigma_n$. For a certain fixed $...
5
votes
0answers
450 views

Shrinkage Estimator for Newey-West Covariance Matrix

I like to apply the Newey-West covariance estimator for portfolio optmization which is given by $$ \Sigma = \Sigma(0) + \frac12 \left (\Sigma(1) + \Sigma(1)^T \right), $$ where $\Sigma(i)$ is the lag ...
5
votes
0answers
304 views

Analyzing the angle between vector of weights and vector of returns in mean-variance optimization

I am using the paper "A Sharper Angle on Optimization" by Golts and Jones (2009) as a basis for my (minor) masters thesis in mathematical finance. The paper focuses on the mean-variance analysis of ...
5
votes
0answers
518 views

Is there a standard method of scaling alpha forecasts to t-cost estimates?

Given a set of monthly alpha forecasts (i.e. standardized z-scores from a multi-factor return model) and a non-linear market impact model (or more specifically, its piecewise-linear approximation), is ...
4
votes
0answers
122 views

How would it be possible to use Dynamic Programming to search a space of investment strategies to find an optimum?

As my question states, the problem I am having is finding a sensible way to search a large space. Any help or insight that could be provided would be hugely appreciated. Currently I am trying to ...
4
votes
0answers
99 views

Optimal mortgage rate strategy

When buying a mortgage, you can choose to "lock in" a rate at any point within 60 days of your closing date. Once locked in, you can't revert. This makes it a secretary problem - in the traditional ...
3
votes
0answers
121 views

Fitting High Frequency Indicators

I have a high frequency time series of the bid and ask prices of a stock recorded on every tick. For each data point I also have a certain indicators that predict the future movement of the price. The ...
3
votes
0answers
70 views

Residual Covariance Matrix, and MVO for Residual Variance and Alpha

My overall goal is to find an efficient frontier using QP in terms of $\alpha$ and residual variance ($\omega^2$) for a portfolio $P$ given a benchmark $B$. We know the equation for residual variance ...
3
votes
0answers
119 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 AR(...
3
votes
0answers
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 ...
3
votes
0answers
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 ...
3
votes
0answers
94 views

Optimizing stochastic functions numerically

Is there an efficient and commonly used optimization method for "more complex" investment strategies. For instance, say you have a function $f(X_1,...,X_n,c,v)$ where the $X_k$'s are your random ...
3
votes
0answers
160 views
3
votes
0answers
501 views

What is the use of the Euler equation in the Ramsey growth model?

I apologise for being brief, but I don't understand how is Euler equation used in the Ramsey growth model. I am reading a textbook "Dynamic General Equilibrium Modeling" and there is mentioned about ...
2
votes
0answers
38 views

Using Market Prices of Bonds to Model the Discount Curve with a Polynomial (Math + R)

I have a small program I'm building to interpolate the discount curve from a portfolio of benchmark bonds. If anyone has any guesses as to whether it's my process, or my code that's messed up I would ...
2
votes
0answers
45 views

Given (past) stock values for N assets, how to find the maximum - theoretical - profit?

In the past few days I have been thinking about a question which seems trivial, yet I can't think of any efficient way to find the optimal solution... Here is the problem: imagine you have a ...
1
vote
0answers
65 views

Optimize a trading strategy created in excel with R

I have created quite a complex back test in excel spanning 15 years with 17 parameters. I would like to optimize the parameters which would give me maximum return given a maximum draw-down percentage. ...
1
vote
0answers
19 views

Continous-time portfolio allocation optimization for a given consumption rate

I have the following PDE $0 = V_t - c(t)V_x - \lambda^2 V_x^2/V_{xx} + rxV_x + 1/2\lambda^2x^2V_{xx}$ where $t\mapsto c(t)$ is some given function and $r,\lambda$ are given constants. If necessary, ...
1
vote
0answers
82 views

How to hedge an ETF position with a basket of its underlying components

In practice, when one takes on a large equity ETF position, I would imagine it's not necessarily "optimal" to hedge using a basket of all the constituents even though that should be a perfect hedge. ...
1
vote
0answers
53 views

Smoothening yield curve by minimizing forward curve slope

I am using government bullet bond data and have bootstrapped a yield curve by solving the following optimization which minimizes unweighted price error: $$\text{min}\sum_i\left(P_i-\sum_t\frac{F_{it}}...
1
vote
0answers
14 views

Is there any theoretical work to find an optimum size for the size of horizon in finite-horizon optimization or control?

we learn a lot about finite and infinite horizon control in dynamic programming. but I was wondering if we want to minimize the cost per time(discrete time) is there any work to find the optimum size ...
1
vote
0answers
97 views

Implementing Minimum Leverage in an SOCP Portfolio Optimization

I'm optimizing a portfolio of n assets and my optimization variable is of the form $$x = [t,w,w_L,w_S]$$ where $$t:= \text{slack variable for turning my QP objective into SOCP constraint}$$ $$w:=\...
1
vote
0answers
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 ...
1
vote
0answers
84 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 ...
1
vote
0answers
1k 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 ...
1
vote
0answers
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 ...
1
vote
0answers
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....
1
vote
0answers
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 ...
1
vote
0answers
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 ...
1
vote
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 <= ...
1
vote
0answers
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 ...
1
vote
0answers
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 ...
1
vote
0answers
543 views

portfolio optimization with a loop

I am attempting to minimize the variance of a 3 stock portfolio using optimization within a loop. What I have done is calculated the stock returns and cov matrix from dates 1980-01-01 to 1989-12-31 ...
1
vote
0answers
389 views

Call options portfolio: what would the underlyings' moments to be maximized?

Let you have only three underlyings, like SPY, TLT and GLD, and you want to buy $n_{1}$ Call options on SPY, $n_{2}$ Call options on TLT and $n_{3}$ Call options on GLD... with a limited budget, that ...
0
votes
0answers
66 views

First step of Black-Litterman portfolio

I tried to implement Black-Litterman model. I have a covariance matrix, market capitalization for each asset. I assume a risk aversion factor to be 10. First I use the following code to get ...
0
votes
0answers
38 views

Bond portfolio optimization

Problem is that I want to match single country term structure return as closely as possible. What would be best way to construct proxy to do this, with less bonds than in original term structure? I ...
0
votes
0answers
19 views

Question in the proof of “Optimization of conditional value-at-risk”

I'm reading the paper "Optimization of conditional value-at-risk" by Rockafellar and Uryasev. The state two theorems within the paper which are proven in the appendix. Let me introduce some notation ...
0
votes
0answers
74 views

Discrete Hedging of Options

Assume that a stock $S_t$ follows simple geometric Brownian motion. Let's say we sold option whose payoff is $f(S_T)$. Now, we are only allowed to trade 2 times in the interval [0,T]. What kind of ...
0
votes
0answers
19 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 ...