Optimization with uncertain variable
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I have an optimization problem of a time-series. I am essentially trying to determine the weights to various investments based on the interest rate that investments pays at the time of the investment ... with the goal of maximizing the interest earned.
Below is a simplification of the problem:
beginarray11
text maximize & sum_i,j=0,0^m,nRATE_ij*INVj \
text where & text i = period in time \
text & text j = type of investment \
text & text RATE = interest rate as a percentage \
text & text INV = amount invested
endarray
The constraints are somewhat complicated and not that material to the question necessarily. The key to the constraints is that the prior periods impact the funds available to invest in the current period.
This problem is quite easy to solve via LPP, if you assume interest rates are known (i.e. you make an interest rate projection).
Still, predicting interest rates is inherently difficult. I have a gut feeling that there must be a way to run multiple interest rate scenarios into a program and find a path (or group of similar paths) that is optimal across the range of rate scenarios considered.
Thus, you would have a path that was resilient regardless of the interest rate outcomes.
Hoping someone could help point me in the right direction in terms of learning. Is this still an LPP problem? Or some other type of algebraic solution? Or should i be considering machine/deep learning techniques?
optimization linear-programming
asked Sep 11 at 3:50
Ry John
12
add a comment |
up vote
0
down vote
favorite
I have an optimization problem of a time-series. I am essentially trying to determine the weights to various investments based on the interest rate that investments pays at the time of the investment ... with the goal of maximizing the interest earned.
Below is a simplification of the problem:
beginarray11
text maximize & sum_i,j=0,0^m,nRATE_ij*INVj \
text where & text i = period in time \
text & text j = type of investment \
text & text RATE = interest rate as a percentage \
text & text INV = amount invested
endarray
The constraints are somewhat complicated and not that material to the question necessarily. The key to the constraints is that the prior periods impact the funds available to invest in the current period.
This problem is quite easy to solve via LPP, if you assume interest rates are known (i.e. you make an interest rate projection).
Still, predicting interest rates is inherently difficult. I have a gut feeling that there must be a way to run multiple interest rate scenarios into a program and find a path (or group of similar paths) that is optimal across the range of rate scenarios considered.
Thus, you would have a path that was resilient regardless of the interest rate outcomes.
Hoping someone could help point me in the right direction in terms of learning. Is this still an LPP problem? Or some other type of algebraic solution? Or should i be considering machine/deep learning techniques?
optimization linear-programming
asked Sep 11 at 3:50
Ry John
12
You may want to look at the portfolio optimization literature . As far as I know in a scenario like yours the approach is to estimate the expected value and the variance for each interest rate and then optimize the objective using the expected values while keeping the risk (defined based on variance) under control using constraints .
– Popescu Claudiu
Oct 14 at 8:51
Thanks for suggestion. I took a look at some forms of stochastic optimization that you're referring to but these seem to be pretty complex problems. I was hoping for a solution with shorter run time. On to the next one!
– Ry John
Oct 14 at 11:34
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I have an optimization problem of a time-series. I am essentially trying to determine the weights to various investments based on the interest rate that investments pays at the time of the investment ... with the goal of maximizing the interest earned.
Below is a simplification of the problem:
beginarray11
text maximize & sum_i,j=0,0^m,nRATE_ij*INVj \
text where & text i = period in time \
text & text j = type of investment \
text & text RATE = interest rate as a percentage \
text & text INV = amount invested
endarray
The constraints are somewhat complicated and not that material to the question necessarily. The key to the constraints is that the prior periods impact the funds available to invest in the current period.
This problem is quite easy to solve via LPP, if you assume interest rates are known (i.e. you make an interest rate projection).
Still, predicting interest rates is inherently difficult. I have a gut feeling that there must be a way to run multiple interest rate scenarios into a program and find a path (or group of similar paths) that is optimal across the range of rate scenarios considered.
Thus, you would have a path that was resilient regardless of the interest rate outcomes.
Hoping someone could help point me in the right direction in terms of learning. Is this still an LPP problem? Or some other type of algebraic solution? Or should i be considering machine/deep learning techniques?
optimization linear-programming
asked Sep 11 at 3:50
Ry John
12
I have an optimization problem of a time-series. I am essentially trying to determine the weights to various investments based on the interest rate that investments pays at the time of the investment ... with the goal of maximizing the interest earned.
Below is a simplification of the problem:
beginarray11
text maximize & sum_i,j=0,0^m,nRATE_ij*INVj \
text where & text i = period in time \
text & text j = type of investment \
text & text RATE = interest rate as a percentage \
text & text INV = amount invested
endarray
The constraints are somewhat complicated and not that material to the question necessarily. The key to the constraints is that the prior periods impact the funds available to invest in the current period.
This problem is quite easy to solve via LPP, if you assume interest rates are known (i.e. you make an interest rate projection).
Still, predicting interest rates is inherently difficult. I have a gut feeling that there must be a way to run multiple interest rate scenarios into a program and find a path (or group of similar paths) that is optimal across the range of rate scenarios considered.
Thus, you would have a path that was resilient regardless of the interest rate outcomes.
Hoping someone could help point me in the right direction in terms of learning. Is this still an LPP problem? Or some other type of algebraic solution? Or should i be considering machine/deep learning techniques?
optimization linear-programming
optimization linear-programming
asked Sep 11 at 3:50
Ry John
12
asked Sep 11 at 3:50
Ry John
12
edited Sep 11 at 3:56
asked Sep 11 at 3:50
Ry John
12
asked Sep 11 at 3:50
Ry John
12
asked Sep 11 at 3:50
Ry John
12
12
You may want to look at the portfolio optimization literature . As far as I know in a scenario like yours the approach is to estimate the expected value and the variance for each interest rate and then optimize the objective using the expected values while keeping the risk (defined based on variance) under control using constraints .
– Popescu Claudiu
Oct 14 at 8:51
Thanks for suggestion. I took a look at some forms of stochastic optimization that you're referring to but these seem to be pretty complex problems. I was hoping for a solution with shorter run time. On to the next one!
– Ry John
Oct 14 at 11:34
add a comment |
You may want to look at the portfolio optimization literature . As far as I know in a scenario like yours the approach is to estimate the expected value and the variance for each interest rate and then optimize the objective using the expected values while keeping the risk (defined based on variance) under control using constraints .
– Popescu Claudiu
Oct 14 at 8:51
Thanks for suggestion. I took a look at some forms of stochastic optimization that you're referring to but these seem to be pretty complex problems. I was hoping for a solution with shorter run time. On to the next one!
– Ry John
Oct 14 at 11:34
You may want to look at the portfolio optimization literature . As far as I know in a scenario like yours the approach is to estimate the expected value and the variance for each interest rate and then optimize the objective using the expected values while keeping the risk (defined based on variance) under control using constraints .
– Popescu Claudiu
Oct 14 at 8:51
You may want to look at the portfolio optimization literature . As far as I know in a scenario like yours the approach is to estimate the expected value and the variance for each interest rate and then optimize the objective using the expected values while keeping the risk (defined based on variance) under control using constraints .
– Popescu Claudiu
Oct 14 at 8:51
Thanks for suggestion. I took a look at some forms of stochastic optimization that you're referring to but these seem to be pretty complex problems. I was hoping for a solution with shorter run time. On to the next one!
– Ry John
Oct 14 at 11:34
Thanks for suggestion. I took a look at some forms of stochastic optimization that you're referring to but these seem to be pretty complex problems. I was hoping for a solution with shorter run time. On to the next one!
– Ry John
Oct 14 at 11:34
add a comment |
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You may want to look at the portfolio optimization literature . As far as I know in a scenario like yours the approach is to estimate the expected value and the variance for each interest rate and then optimize the objective using the expected values while keeping the risk (defined based on variance) under control using constraints .
– Popescu Claudiu
Oct 14 at 8:51
Thanks for suggestion. I took a look at some forms of stochastic optimization that you're referring to but these seem to be pretty complex problems. I was hoping for a solution with shorter run time. On to the next one!
– Ry John
Oct 14 at 11:34