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Portfolio Optimization Artificial Intelligence in Finance
Zsolt Bihary (Morgan Stanley)
2013, Budapest
Structuring (Securitization)
Pool of
Loans
Cash-flow Bank
Bank wants to • Get rid of risk • Realize future cash-flow now
Investors
Investors want to • Invest in the long run • with different risk
Structuring (Securitization)
A
B
D
C
Pool of
Loans
Cash-flow
Wate
r-fall
Investors
Investors
Investors
Bonds
Bank
The Structuring Problem
A
B
D
C
Pool of
Loans
Cash-flow
Wate
r-fall
Bonds
How to choose bond sizes? Bank is interested in great bond sizes and high ratings. Regulators seek to limit bond sizes before giving high ratings.
Bank
The Black Box Simulator
A
B
D
C
Black Box Simulator
• Pricing • Scenario 1 • Scenario 2 • Scenario 3 • Scenario 4
INPUT
Bonds
OUTPUT
Structure (bond sizes)
• Proceeds • Scenario 1 result • Scenario 2 result • Scenario 3 result • Scenario 4 result
The Black Box Simulator
A
B
D
C
Black Box Simulator
• Pricing • Scenario 1 • Scenario 2 • Scenario 3 • Scenario 4
INPUT
Bonds
OUTPUT
Structure (bond sizes)
• Proceeds • Scenario 1 result • Scenario 2 result • Scenario 3 result • Scenario 4 result
We want to maximize proceeds, under the constraint that the structure passes all stress-test scenarios.
Nature of the Optimization Problem
• Objective function and constraints evaluated by Black Box (no gradients available)
• Objective function and constraints evaluated simultaneously (unknown constraints)
• Constraints returned as pass/fail Booleans (no differentiable discriminant functions)
• Black Box is very slow (we can afford only 5 iterations)
• We can run Black Box parallel on 20 servers
Synthetic Example
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
A bond size
B bond size
A (20%)
B (50%)
D (30%)
Example structure
Synthetic Example
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
A bond size
B bond size
A (20%)
B (50%)
D (30%)
Example structure
Global optimum
Synthetic Example
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
A bond size
B bond size
A (20%)
B (50%)
D (30%)
Example structure
Global optimum
Local optimum
Reinforcement Learning
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
Reinforcement Learning
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
Initially, put down random structures
Reinforcement Learning
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
At each iteration, new structures are selected
based on information on previous structures
Reinforcement Learning
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
At each iteration, new structures are selected
based on information on previous structures
Reinforcement Learning
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
At each iteration, new structures are selected
based on information on previous structures
Reinforcement Learning
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
At each iteration, new structures are selected
based on information on previous structures
Surrogate Model Approach
Initial Random Structures
Surrogate Model New Design Structures
Best Structure Found
Black Box Simulator
Results on Structures
Surrogate Model Approach
Initial Random Structures
Surrogate Model New Design Structures
Best Structure Found
Black Box Simulator
Results on Structures
Objective function:
Linear Regression
Constraints:
Support Vector
Machine (SVM)
Support Vector Machine (SVM)
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
Gives a surrogate model for the
pass – fail boundary
Support Vector Machine (SVM)
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
With more points, SVM gives more
and more accurate boundary
Support Vector Machine (SVM)
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
With more points, SVM gives more
and more accurate boundary
Support Vector Machine (SVM)
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
With more points, SVM gives more
and more accurate boundary
Pass Probability
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
SVM maps out the pass probability
in structure space
Pass Probability
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
With more points, pass probability
map becomes more and more accurate
Pass Probability
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
With more points, pass probability
map becomes more and more accurate
Pass Probability
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
With more points, pass probability
map becomes more and more accurate
Expected Improvement
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
Surrogate model maps out the most
promising regions of structure space
Expected Improvement
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
With more and more points, surrogate
model zeros in to the optimal region
Expected Improvement
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
With more and more points, surrogate
model zeros in to the optimal region
Expected Improvement
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
With more and more points, surrogate
model zeros in to the optimal region
Conclusion
Using Machine Learning techniques
on the Portfolio Structuring Problem,
we could provide a useful tool
for our structuring business
Thank you for your attention
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