# 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.

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### 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 ...
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### 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. ...
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### 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 ...
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### 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-...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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:=\...
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### 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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### 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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### 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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### 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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### 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....
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### 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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### 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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### 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 <= ...
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### 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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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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 ...