Decision analysis
Shauna Phillips
School of Economics
Copyright By PowCoder代写 加微信 powcoder
AREC3005 Agricultural Finance & Risk
, file photo: Reuters, file photo
Dr Shauna Phillips (Unit Coordinator) Phone: 93517892
R479 Merewether Building
COMMONWEALTH OF AUSTRALIA Copyright Regulations 1969 WARNING
This material has been reproduced and communicated to
you by or on behalf of the University of Sydney
pursuant to Part VB of the Copyright Act 1968 (the Act).
The material in this communication may be subject to copyright under the Act. Any further reproduction or communication of this material by you may be the subjectofcopyright protectionundertheAct.
Do not remove this notice.
Outline of decision process
1. Identify decision problem
2. Structure problem for analysis
3. Dissect problem into components
7. Monitor/Review
4a. Assess beliefs about 4b. Assess preferences for
uncertainty
consequences
5. Decision-making
6. Implement indicated decision
› Decision analysis is the family of methods which attempt to create structured approaches to decision-making
› Sometimes called decision-making frameworks (benefit-cost analysis, decision trees, simulation, exposure assessment, control charts, payoff matrices, portfolio theory, state-contingent analysis, etc).
› Any of these frameworks may be applied at greater or lesser levels of sophistication
– Formalised benefit-cost analysis vs. ‘pro-con’ analysis
› Appropriate framework depends on the context of the risky decagons that need to be made.
1. Decision problems
› Complexity is an omnipresent feature of decision problems involving uncertainty. This might mean:
– The available information is incomplete
– The problem involves multiple and conflicting objectives
– There are multiple stakeholders
– We have inter-linked decision problems
– The decision context may be dynamic and turbulent
– Solutions may involve irreversibilities or hysteretic properties
2. Structure problem for analysis (what are the relevant values?)
Total economic value
Non-use value
Option value
Existence value
Bequest value
Direct use
Indirect use
Values and uncertainties
› Different components of Total Economic Value will become more/less dominant under different forms of uncertainty
– Under certainty, option values are zero
– Option values represent the trade-offs between acting
now, given uncertainties, versus acting later
– Option values will dominate under extreme uncertainty
3. Dissect problem
› What are we examining?
› How do we arrange the problem into an examinable form?
› Do we need to make some assumptions in order to proceed? › What options available to us?
› At what level do we analyse the problem?
4a. Beliefs about uncertainty
› Decision analysis is based on the proposition that a ‘good’ decision is one that is consistent with what the decision-maker believes about the uncertainties
› Beliefs regarding the structure (model) of uncertainties is usually framed as being subjective or objective
– In all cases, we are adopting a model of uncertainty which satisfies some belief
– Arguably, the extent to which these beliefs are satisfied is subjective
– Nevertheless, we will proceed with the distinction that objective beliefs are those where our model of uncertainty is the best available, given the data we have at hand
4b. Assess preferences for consequences
› At the social level, different people will have different preferences over outcomes, possibly in direct conflict
– Might have very different attitudes to risk
– Social welfare functions can help resolve group preferences over outcomes
› Capturing preferences at the individual level is easier
– We can elicit the preference structure, including attitudes toward risk – Risk averse ; risk loving ; risk neutral
Foot-and-mouth disease UK 2001
› “crisis in British agriculture and tourism ..2,026 cases of the disease in farms …6 million cows and sheep were killed…the crisis was estimated to have cost the United Kingdom £8bn (US$16bn)”. (Source: Wikipedia)
Simple risk decision example [Hardaker et al.(2004)]
› EU Dairy farmer facing foot-and-mouth disease risk Source: BBC 2016 http://www.bbc.com/news/magazine-35581830
› Policy response to outbreak
– Suspicion of infection, results in animal destruction – Government pays
compensation
– Freeze on movement of animals and mandated on-farm actions – Government does not compensate
– No livestock on farm for at least six months – Government does not compensate
– 2016 FMD outbreak in UK cost public sector £ 3bn and private sector £5bn
Source: BBC 2016 http://www.bbc.com/news/magazine-35581830
Simple risk decision example [Hardaker et al.(2004)]
› Let’s say there is an insurance product which provides coverage against un-compensated losses arising from an outbreak
Simple risk decision example
› Structuring problem for analysis – can use an influence diagram, which includes:
– Decision nodes: existence of options (rectangles)
– Chance nodes: uncertainty with alternative outcomes (ovals)
– Consequence nodes: consequences of decisions and uncertainties (diamonds)
Simple risk decision example
Chance node Decision node
Consequence node
Simple risk decision example
› Alternative structuring of problem for analysis – can use decision tree representation:
– Decision forks: existence of options (decision nodes are rectangles)
– Chance (event) forks: uncertainty with alternative outcomes (chance nodes
are circles)
– Consequences terminals: consequences of decisions and uncertainties (terminal nodes are triangles)
Payoffs ($’000)
Net Assets
Insurable losses
Insurance premium
No insurance
Simple risk decision example
Decision fork Decision node
Chance node Chance/Event fork
Terminal/Consequence node
Simple risk decision example
Simple risk decision example (cont)
› Can’t say much more without information about likelihoods of various outcomes
– Could insure, but if the likelihood of outbreak is low, insurance might not be worthwhile
– Will work through example below that develops methods to analyse by assuming model of uncertainties
– Otherwise, we can use the method of certainty equivalents to the analyse problem
Simple risk decision example (cont)
› Certainty equivalent (CE): the sum of money that would need to be paid (for sure) to the farmer to make them indifferent between facing the risk (i.e. the risky prospect) or accepting the certain payment
– Effectively, the farmer is selling the gamble – what is the minimum sure price for which the farmer would be willing to sell a desirable risky prospect?
– Alternatively, what is the highest sure payment the farmer would make to get rid of an undesirable risky prospect?
– CEs will vary between gambles (different risks) and people (different attitudes to risk)
Simple risk decision example (cont)
› Could ask the farmer to express these CEs by sequential, backward questioning
– Expressed in a payoff table, let’s start by assuming a disease outbreak has occurred, so the sure sum relates to two outcomes
Simple risk decision example (cont)
Simple risk decision example (cont)
› If we offered a sure sum of $300,000, then we would expect rejection, since $300,000 is the worst-case scenario – there is a chance (i.e. positive probability) of $490,000
› If we offered $490,000, we would expect acceptance, since this value is equal to the best possible outcome
› Somewhere between $300,000 and $490,000, there is a reversal in preference over taking the gamble or the ‘sure sum’
Simple risk decision example (cont)
opt for risky prospect
opt for sure sum
if opts for sure sum ( thinks 490 less likely)
so next x should be a lower value, say 380
if opts for risky (thinks 490 likely)
so next x should be a higher value
Simple risk decision example (cont)
› In principle, we keep varying the offer between $300,000 and $490,000 until we find a point of indifference
– Identifying this point of indifference reveals the farmer’s CE
› Let’s say the CE was identified as $384,000 – we can further simplify the decision tree:
Simple risk decision example (cont)
› Repeat the CE elicitation exercise to further simplify the tree (at the first decision node)
› CE must be between $500,000 and $384,000
– If the CE is less than $492,800 → take out insurance – If the CE is more than $492,800 → take the gamble
Elicit CE for this gamble
Steps in decision tree analysis
1. Calculate money payoffs for each terminal node, given relevant information
2. Working backwards (i.e. solve by using backward induction) from the terminal branches, reduce the tree by establishing CE values for each chance node
3. When get to a decision node, identify the highest CE value, and eliminate all lower CE value options
4. Plot optimal pathway by following sequence of highest CE values
Decision making
› Information is costly and the costs of making a ‘mistake’ vary, so decisions processes can occur at various levels of intensity
– Routine: decide quickly and without deliberation
– Imagination: starting to visualise alternative future events and attendant
consequences
– Reasoning: costly and complex decisions involves conscious and methodical deliberation
Decision-biases
› Reasoning is supposed to help us avoid decision-biases, which may steer people towards less optimal decisions and, possibly, ‘mistakes’
– Heuristics as a way of simplifying uncertainty
– Paradigm seeking behaviour: models of response to uncertainty from similar
people to themselves
– Paradox of choice (a.k.a. excessive choice): when presented with a lot of choice, we can be reluctant to make a decision in case we regret it…since we had so many choices
– Loss aversion: weight losses more heavily than equivalent gains – over weighting bad information
– Confirmation biases: search for information that confirms hypothesis more actively than search for information that disproves it – selective use of information
Decision-making frameworks
› Reasoning in decision making is captured in formalised tools for conscious and systematic deliberation, which can be classified based on the idea of decision making meta-frameworks (Randall et al. 2012)
– Benefit-cost analysis: reconciliation of all the relevant benefits and costs, subject to uncertainties, over time
– Adaptive management: initiate processes to gather relevant information, proceed with precaution, and update management strategy as new information becomes available (precautionary principle-”look before you leap”- avoid immediate adoption of technology that may turn out to be harmful-if you “leap” too soon costs may be enormous if technology is embedded in economy – ( eg asbestos, thalidomide)
Cost-benefit Adaptive
analysis management
Cost-benefit Adaptive
analysis management
Randall (2011):
Outcomes are generated by a random process
Cost-benefit Adaptive
analysis management
Randall (2011):
Outcomes are generated by a random process
We do not understand the system that generates outcomes
Cost-benefit Adaptive
analysis management
Randall (2011):
Outcomes are generated by a random process
We do not understand the system that generates outcomes
The system that generates outcomes is itself changing
Example decision framework: real options analysis
› Real Options thinking
– Are there uncertainties? If yes, then we proceed in a way that keeps our options
› Computational Real Options (Sanderson et al. 2015)
– Stochastic dynamic optimal stopping problem
– Uses biophysical data to model the stochastic process that generates net benefits – Quantifies the option values, critical regime thresholds and transition probabilities
Introduction to real options (RO)
› RO extends standard economic analysis of investment decisions (cost- benefit analysis).
› RO improves representation of uncertainty in decision making.
› Important as some adaptation decisions can be costly to reverse or
irreversible.
› RO allows us to understand timing of adaptation decisions (modelled as switches from one production regime to another): 2 production regimes: wheat the sheep:
Australian wheat belt
Source: Adapted from ABARES
Implementing a Real Options Analysis
› Step 1: gather data on the system, estimate appropriate stochastic process
› Step 2: identify decision options
› Step 3: use estimated process and other cost information to estimate
option values and regime thresholds
› Step 4: use parts of 1 and 2 to estimate regime transition probabilities
Step 1: data
Step 1: Stochastic process
dxt =−bxt −dt+dzt Orroroo
dxt =−bxt −(+t)dt+dzt
X data in levels : Xt
• X data with 1 period lag : Xt-1
• X data in first differences : dXt = ΔXt = Xt – Xt-1
Step 2. Decision tree representation of problem
Stay in wheat
Stay in bank
5% interest
Enter sheep
Enter wheat
Stay in wheat
Negative GM
Initially, all money is in the bank
Enter sheep
Step 2. Decision tree representation of problem
Stay in wheat
Stay in sheep
Exit to bank
5% interest
Enter sheep
Negative GM
Stay in sheep
Exit to bank
5% interest
Option values
› Option values (w) are estimated at each decision node, given the information we have on the stochastic returns (gross margins) under each option
› We also get some information about the gross margin thresholds, which, when crossed, initiate a particular decision
– This is more complicated than the earlier example, because we are trying to compare two uncertain options
Step 3 & 4: Alternative Production Regimes
Step 3 & 4: Alternative Production Regimes
Entry to wheat: w = $211
threshold = $497
5 year transition probability = 38%
Step 3 & 4: Alternative Production Regimes
Exit wheat to enter sheep: w = $161
threshold = $128
5 year transition probability = 9%
Step 3 & 4: Alternative Production Regimes
Exit sheep, move to beach: w = $5
threshold = $29
5 year transition probability = 1%
› Hardaker, Huirne and Anderson (2004) Coping with Risk in Agriculture, CAB International.
– Chapter 2
› Sanderson et al. (2015) A real options analysis of Australian wheat production under climate change. Australian Journal of Agricultural and Resource Economics, 60 (1).
References
› Randall (2011) Risk and precaution. Cambridge University Press, UK.
› Randall, A., Capon, T., Sanderson, T., Merrett, D. and Hertzler, G. “Understanding end-user decisions and the value of climate information under the risks and uncertainties of future climates”, Report commissioned by the National Climate Change Adaptation Research Facility.
程序代写 CS代考 加微信: powcoder QQ: 1823890830 Email: powcoder@163.com