Tommelfingerregler vs. optimering

Wealth Planning and Machine
Learning
Kourosh Marjani Rasmussen,
Schantz (kmr@schantz.com)
DTU
(kmra@dtu.dk)
1. september 2015
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Normative vs. Positive Economics
• Normative Economics:
“1.000.000 people can’t be wrong.”
• Positive Economics:
“Yes, they can, and I can prove it.”
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Life cycle financial planning
Phase 1
Phase 2
25
Depletion
Consolidation
Build up
Age:
Phase 3
45
65
85
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Planning ingredients
The household economy
Disposable income
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Optimization Model (Positive Economics)
Objective: Find the largest disposable income for the entire lifecycle
given some percentage reduction at a given year
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The objective functions
Objective Function 1:
Respect the disposible income up to the retirement year. Thereafter,
maximize the smallest disposible income for a given year.
𝒎𝒂𝒙𝒊𝒎𝒊𝒛𝒆 𝐹𝑖𝑥𝑒𝑑𝐴𝑁𝑃
w.r.t.
𝐹𝑖𝑥𝑒𝑑𝐴𝑁𝑃 ≤
𝐴𝑁𝑃𝑡 = 𝑋𝑡
𝐴𝑁𝑃𝑡
𝑎𝑙𝑝ℎ𝑎𝑡
∀ 𝑡 ∈ 𝑡𝑖𝑚𝑒 𝑖𝑓 𝑅𝑒𝑡𝑖𝑟𝑒𝑚𝑒𝑛𝑡𝑇𝑖𝑚𝑒𝑡 = 1
∀ 𝑡 ∈ 𝑡𝑖𝑚𝑒 𝑖𝑓 𝑊𝑜𝑟𝑘𝑇𝑖𝑚𝑒𝑡 = 1
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The objective functions
Objective Function 2:
Obtain the maximum disposible income for the entire period.
𝒎𝒂𝒙𝒊𝒎𝒊𝒛𝒆 𝐹𝑖𝑥𝑒𝑑𝐴𝑁𝑃
w.r.t
𝐹𝑖𝑥𝑒𝑑𝐴𝑁𝑃 ≤
𝐴𝑁𝑃𝑡
𝑎𝑙𝑝ℎ𝑎𝑡
∀ 𝑡 ∈ 𝑡𝑖𝑚𝑒
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The objective functions
Objective Function 3:
Maximize the disposible income prior to retirement while respecting a given
target during the retirement period.
𝒎𝒂𝒙𝒊𝒎𝒊𝒛𝒆 𝑌
w.r.t
𝐴𝑁𝑃𝑡 = 𝑋𝑡 + 𝑌
𝐴𝑁𝑃𝑡 ≥ 𝑇𝑎𝑟𝑔𝑒𝑡𝑡
∀ 𝑡 ∈ 𝑡𝑖𝑚𝑒 𝑖𝑓 𝑊𝑜𝑟𝑘𝑇𝑖𝑚𝑒𝑡 = 1
∀ 𝑡 ∈ 𝑡𝑖𝑚𝑒 𝑖𝑓 𝑅𝑒𝑡𝑖𝑟𝑒𝑚𝑒𝑛𝑡𝑇𝑖𝑚𝑒𝑡 = 1
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Social Benefits
1) 𝐼𝑛𝑐𝑜𝑚𝑒 = 𝑃𝐼1𝑡 + 𝑃𝐼2𝑡 + 𝑃𝐼3𝑡
∀ 𝑡 ∈ 𝑡𝑖𝑚𝑒
2) 𝑃𝐼1𝑡 ≤ 𝐴𝑡
∀ 𝑡 ∈ 𝑡𝑖𝑚𝑒
3) 𝑃𝐼2𝑡 ≤ 𝐵𝑡
∀ 𝑡 ∈ 𝑡𝑖𝑚𝑒
4) 𝑃𝐼3𝑡 ≤ 𝑃𝐼3_Bin𝑡 ∙ 𝑀
∀ 𝑡 ∈ 𝑡𝑖𝑚𝑒
5) 𝐵𝑡 ∙ (1 − 𝑃𝐼3Bin 𝑡 ) ≥ 𝐵𝑡 − 𝑃𝐼2𝑡
∀ 𝑡 ∈ 𝑡𝑖𝑚𝑒
6) 𝑆𝑜𝑐𝑖𝑎𝑙𝐵𝑒𝑛𝑒𝑓𝑖𝑡𝑡 = 𝑀𝑎𝑥𝑃𝑎𝑦𝑚𝑒𝑛𝑡𝑡 − 𝑃𝐼2𝑡 ∙ 𝑅𝑒𝑑𝑢𝑐𝑡𝑖𝑜𝑛𝑅𝑎𝑡𝑒𝑡
∀ 𝑡 ∈ 𝑡𝑖𝑚𝑒
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Constraints
•
Pensions
 Different tax regimes for different pensionschemes
 Specific cashflow restrictions
•
Social benefits
 Six different types
 Interaction with different sources of income
•
Loans
 Mortgage loans
 Consumption loans
 Bank loans
 Reverse mortgages
•
Tax




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•
Companies
Income tax
Capital gain tax
Stock tax
Pension tax
Tax rebates
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We can model all this!
Model Statistics:
The objective function is to maximize the family´s disposable income with
respect to +300 generic constraints
The model is a mixed integer program solved with GAMS/CPLEX.
Approximate number of constraints: 100.000
Approximate number of variables: 200.000
Approximate number of binary variables: 10.000
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Or can we?
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And can we get people to use it?
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But can we model human behavior
We learn gradually – so can our models.
Ex: Google face recognition network trained on millions of
pictures.
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Mini Project: Wealth Planning & Machine Learning
Machine learning can cluster clients into similar groups.
Human interaction with the system will be captured.
(Normative Economics)
The optimization model will be enhanced with time.
(Hybrid Economics: Do what works and teach what is right!)
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KOUROSH MARJANI
RASMUSSEN
M: +45 40866164
E: KMR@SCHANTZ.COM
SCHANTZ A/S
KIGKURREN 10
DK-2300 KØBENHAVN S
T: +45 3332 1984
WWW.SCHANTZ.COM
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