New Car Smell

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New Car Smell

• Computational Finance Final Project
• 12/06/06
• Philip Kromer
• Chris Wieland

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Optimal Car Replacement
Cost to maintain an a-year old car
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Optimal Car Replacement
Discounted value of a car that is a1 years old
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Optimal Car Replacement
Cost to maintain a new car
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Optimal Car Replacement
Difference between the price of a used and new car
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Optimal Car Replacement
Discounted value of a 2-year old car
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Maintenance
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Maintenance
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Basic Formula
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Car Death
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Junkyard
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Junkyard
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Basic Formula
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Transaction Costs and Buy/Sell Spread
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Annoyance Factor
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Opportunity Costs
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Opportunity Costs
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Purchasing Freedom
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Full Model (Honda)
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Full Model (Honda)
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Full Model (Honda)
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Full Model (Ford)
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Full Model (Ford)
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Full Model (Ford)
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Entering the Market
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Oh! That New Car Smell!
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Optimal Asset Replacement

• Each year, you must keep or replace your car that
  is a-years old
• P(a) cost to operate car for that year
• c price of a new car
• What replacement policy minimizes costs?

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Optimal Asset Replacement

• Infinite horizon, deterministic model
• State Variable a ? 1,2,,n is the car age
• Action Variable x ? keep, replace
• Transition Function g(x)
• Reward Functionf(a,x)
• Bellman Equation

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Solution Algorithm

• 0. Initialization Specify rewards, discount,
  convergence tolerance,? and initial guess,v.
• 1. Function Iteration Update the value function
• 2. Termination Check If , set
• And stop otherwise return to 1.