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4. Decision & Risk Analysis (Subject) / Decision Tree Analysis & LP (Lesson)

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  • Improve Estimates on Probability Consult all relevant sources Historical data Expert opinions Government forecasts
  • EMV Maximiser An EMV maximizer, by definition, is indifferent when faced with the choice between entering a gamble that has a certain EMV and receiving a sure dollar amount in the amount of the EMV. For example, consider a gamble where you flip a fair coin and win $0 or $1000 depending on whether you get a head or a tail. If you are an EMV maximizer, you are indifferent between entering this gamble, which has EMV $500, and receiving $500 for sure.
  • One-Way Sensitivity Analysis Why? Probabilities in decision analysis are often best guesses Observe changes in profit due to changes in assumptions Identify main uncertainty driver Will optimal decision continue to be optimal as one or more inputs changes? Look at client assumption – 50% Look at Cross-Point: 52% ANSWER: Client should decide to do X if estimated probability for Y is more than 43%. He should revise his best-guesses probabilities Consult all relevant sources Historical data Expert opinions Government forecasts ANSWER: How Sensitive is the recommendation? Small Distance: The Decision X is very sensitive to U1. Only small change in this assumption and the Optimal Decision Dominated: Easy decisions - stochastically dominant, for every level, the chance of making a level, there is a higher chance of making this amount of money for the Boss than with the Sales Person    
  • Decision Trees Graphical tool for analysing decisions made over time Helps to structure the outcomes over time Need information on the probability of each outcome Shows how decisions depend on uncertain outcomes Show sequence of events (decisions, outcomes, probabilities and monetary values)
  • Monty Hall Problem Game with Uncertainty involved - Derliberate actions add value When we take away one envelope, there is more information about doors 2 and 3 that was not available at the beginning of the game, when the door 1 was chosen by the player Host's deliberate action adds value to the door he did not choose to eliminate, but not to the one chosen by the originally chosen (Deliberate actions increases the chance to 2/3 Actual Deal - Swap this and the torn letter (2/3) chance against the last one (1/3)Before Random: 50:50 chance Contestants who switch have a 2/3 chance of winning,while contestants who stick to their initial choice have only a 1/3 chance. If we play the game100 times and everytime says swap, then she wins 66.667 % of all times
  • EVPC The maximum client should be willing to pay for Perfect Control EV with Perfect Control - Decrease Uncertainty Node to 0% EV Base Max. Willingsness To Pay = EV (Perfect Control) – EV(Base) RISK PROFILE IMPCAT: Higher due to lower returns because of additional cost
  • Two-Way Sensitivity Analysis Shows the optimal decision and EV changes with simultaneously varying probability combinations. The more drastic colors change, the more sensitive is the optimal decision to % 
  • EVPI The maximum client is willing to pay for perfect information Time-Extension, Detector Investment (1) EV with Perfect Information = Only decide (Yes) if wanted event happens; if not, do not. a. If event 1, then we do b. If event 2, then we do Y -> SKIP THE UNCERTAINTY NODE - (2)  EV Base (3)  Max. Willingsness To Pay = EVPI – EV(Base) RISK PROFILE: Distinguish if for free or not
  • EVSI: Expected Value of Sample Information -3.3 EVSI: Expected Value of Sample Information: The maximum client is willing to pay for sample information Costly Seismic test to get an estimate -> never perfect information Bayes Rule: i.         Two answers YES & NO ii.         For each answer CORRECT & INCORRECT
  • Certainty Equivalent (CE) The amount that makes you indifferent between receiving that amount and a risky payoff EV < CE you are risk averse EV > CE you are risk-seeking EV = CE you are risk neutral Most decision-makers are not consistent; their attitude towards risk depends on the amount at stake
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  • EVPI - ANSWER Free Lunch vs. Costly FREE LUNCH ANSWER: When we make a Decision, we only drill when event 2 occurs. The value of a detector in this project is {EVPI}. His Willingness to Pay should be X RISK PROFILE IMPACT: Radical Change in the Risk Profile; Completely eliminate Downside risk. There is no chance that the client would lose money on this prospect if they would have a free detector COST FOR INFORMATION – Compare to Cost ! ANSWER: When we make a Decision, we only drill when event 2 occurs. The test would increase the EV of the prospect from X to Y. The rest is therefore worth {EVPI}, which is more than its cost. RISK PROFILE IMPACT: Improvement of Risk Profile. Downside Risk: When taking the test, the % of losing money increased, because more money was invested.However, the probability of losing $M is reduced to 36%, which has a relatively greater effect on overall risk. Upside Risk: is only slightly affected by the cost. 
  • Shadow Price  The Shadow price is the impact on the client objective by moving the constraint one unit up or down.   The additional investment required now more in order to have 1 million more available in year 4. The upfront investment could be reduces by {Shadow Price} if we would be fine with 1 M less in year 4. If my requirement is somewhere between {450+ Allowable De-/Increase}, I have to invest {Shadow Price} more to generate 1 more M tomorrow. 
  • Relaxing Constraints: Additional Offer ADDITIONAL OFFER? Shadow price > 0? - Is it worth it or not to add clay? Shadow Price > Cost? Is the additional profit higher than its price Allowable Increase = Is the additional increase within the Limit? Yes? Buy the whole 20! No? I would buy the {allowable increase} and would re-run the model and check what the new Shadow Price. If it is greater than our cost, I would still buy it.
  • Shadow Price - Relaxing Constraints Method 1 = Method 2 à Method 1 – Method 2 = 0 Check what they produce right now in Constraints-> 0 Check how much profit would increase if we relax constraint? Shadow Price > 0 ? Any Cost? To what extent? TOTAL PROFIT = Allowable Increase * Shadow Price 
  • LP Problem Definition Max Limited Resources, given subject to LESS Constraints <= Min Limited Resources, given subjects to MORE Constraints >= 

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