Conditional Value at Risk (CVaR) Model by GAMS

GAMS
1

Dear Gams Friend.

If there is anybody here who models Conditional value at Risk Models by GAMS.

My confusion is on definition of conditional value at Risk. My confusion is given below-

I want to minimize worst case cost and write CVaR as
CVaR =A+(1/1-B) *Sum(s,P(s)*V(s)),

where , A=VaR;
B= confidence level .
Now when I solve the model using B=0.99 or 0.95 or 0.90, I ger VaR=CVaR which is not acceptable. also we get same tail cost for every scenario after solving the model if we such values of B.

When I use B=0.01 or 0.05 or 0.1 then , I get CVaR is greater than VaR that is acceptable and the solution is reasonable.

My question is regarding B. If I write the CVaR equation like above, what should the value of B? In particular, whether 1-B=99% for example Or 1-B=1%.

Please help me clarify on this.

Regards,
Syed

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2

Daer Syed Ali,

Can write simple example of your objective?

Regards


On Sun, Dec 1, 2013 at 10:48 AM, Syed Ali wrote:

Dear Gams Friend.

If there is anybody here who models Conditional value at Risk Models by GAMS.

My confusion is on definition of conditional value at Risk. My confusion is given below-

I want to minimize worst case cost and write CVaR as
CVaR =A+(1/1-B) *Sum(s,P(s)*V(s)),

where , A=VaR;
B= confidence level .
Now when I solve the model using B=0.99 or 0.95 or 0.90, I ger VaR=CVaR which is not acceptable. also we get same tail cost for every scenario after solving the model if we such values of B.

When I use B=0.01 or 0.05 or 0.1 then , I get CVaR is greater than VaR that is acceptable and the solution is reasonable.

My question is regarding B. If I write the CVaR equation like above, what should the value of B? In particular, whether 1-B=99% for example Or 1-B=1%.

Please help me clarify on this.

Regards,
Syed

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3

Thanks for your reply. I again run the model. I observed that upto confidence level 0.70, The CVaR is greater than VaR. for a confidence level greater than 0.70
CVaR equals VaR.

In theory, we see that CVaR is greater than equal to VaR. Depending on the model and data, may be CVaR equals VaR at some point. I hope, you might interpret the situation better.
I have provided an example of my model.

Regards,
Syed


On Sunday, December 1, 2013 6:05:03 PM UTC+9, ARYABOD wrote:

Daer Syed Ali,

Can write simple example of your objective?

Regards


On Sun, Dec 1, 2013 at 10:48 AM, Syed Ali wrote:

Dear Gams Friend.

If there is anybody here who models Conditional value at Risk Models by GAMS.

My confusion is on definition of conditional value at Risk. My confusion is given below-

I want to minimize worst case cost and write CVaR as
CVaR =A+(1/1-B) *Sum(s,P(s)*V(s)),

where , A=VaR;
B= confidence level .
Now when I solve the model using B=0.99 or 0.95 or 0.90, I ger VaR=CVaR which is not acceptable. also we get same tail cost for every scenario after solving the model if we such values of B.

When I use B=0.01 or 0.05 or 0.1 then , I get CVaR is greater than VaR that is acceptable and the solution is reasonable.

My question is regarding B. If I write the CVaR equation like above, what should the value of B? In particular, whether 1-B=99% for example Or 1-B=1%.

Please help me clarify on this.

Regards,
Syed

–
example CVaR.docx (35.3 KB)

4

Dear Syed

Im facing a similar problem did you find a solution to this issue ?
Regards





El domingo, 1 de diciembre de 2013 03:48:36 UTC+1, Syed Ali escribió:

Dear Gams Friend.

If there is anybody here who models Conditional value at Risk Models by GAMS.

My confusion is on definition of conditional value at Risk. My confusion is given below-

I want to minimize worst case cost and write CVaR as
CVaR =A+(1/1-B) *Sum(s,P(s)*V(s)),

where , A=VaR;
B= confidence level .
Now when I solve the model using B=0.99 or 0.95 or 0.90, I ger VaR=CVaR which is not acceptable. also we get same tail cost for every scenario after solving the model if we such values of B.

When I use B=0.01 or 0.05 or 0.1 then , I get CVaR is greater than VaR that is acceptable and the solution is reasonable.

My question is regarding B. If I write the CVaR equation like above, what should the value of B? In particular, whether 1-B=99% for example Or 1-B=1%.

Please help me clarify on this.

Regards,
Syed

–
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5

Dear Juliana,

Technically, VaR = CVaR when B is greater than 0.861. This is because the number of samples(scenarios) are few, so we need much more samples.

Here’s one more thing.

As you probably know,

V(s) >= f(s)-A.

f(s) = total cost in scenario “s.”
.

Regards,
Syed


On Tue, Aug 12, 2014 at 8:26 PM, Juliana wrote:

Dear Syed

Im facing a similar problem did you find a solution to this issue ?
Regards





El domingo, 1 de diciembre de 2013 03:48:36 UTC+1, Syed Ali escribió:

Dear Gams Friend.

If there is anybody here who models Conditional value at Risk Models by GAMS.

My confusion is on definition of conditional value at Risk. My confusion is given below-

I want to minimize worst case cost and write CVaR as
CVaR =A+(1/1-B) *Sum(s,P(s)*V(s)),

where , A=VaR;
B= confidence level .
Now when I solve the model using B=0.99 or 0.95 or 0.90, I ger VaR=CVaR which is not acceptable. also we get same tail cost for every scenario after solving the model if we such values of B.

When I use B=0.01 or 0.05 or 0.1 then , I get CVaR is greater than VaR that is acceptable and the solution is reasonable.

My question is regarding B. If I write the CVaR equation like above, what should the value of B? In particular, whether 1-B=99% for example Or 1-B=1%.

Please help me clarify on this.

Regards,
Syed

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Have fine.
Warm Regards,
Syed Mithun Ali, Assistant Professor, Department of Industrial and Production Engineering, Bangladesh University of Engineering and Technology. Dhaka-1000, Bangladesh.
Mobile no: +8801916034096/+8801718370993
Alternative email: mithun@ipe.buet.ac.bd
http://www.buet.ac.bd/ipe/faculty1.html


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