# 计算机代考 AREC3005 Agricultural Finance & Risk – cscodehelp代写

Shauna Phillips

School of Economics

Quantifying uncertainty(II)

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AREC3005 Agricultural Finance & Risk

, file photo: Reuters, file photo

Dr Shauna Phillips (Unit Coordinator) Phone: 93517892

R479 Merewether Building

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Recall the disease outbreak problem

› Decision tree

Subjective probabilities

don’t insure

no outbreak (P=0.94) $500

bans only (P=0.5)

P(outbreak & bans=0.03) $490

don’t insure

outbreak (P=0.06)

› E(net asset | insured)= 0.94*492.8+0.06*492.8=$492.8

› E(net asset | uninsured)= 0.94*500+0.03*490+0.03*490=$493.7

$300 Slaughter (P=0.5)

P(outbreak & slaughter=0.03)

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

Recall the disease outbreak problem

› Decision tree

no outbreak (P=0.94) $500

don’t insure

outbreak (P=0.06)

› E(net asset | insured)= 0.94*492.8+0.06*492.8=$492.8 › E(net asset | uninsured)= 0.94*500+0.06*384=$493.04

Using CE version of the same problem

Subjective probabilities

don’t insure

no outbreak

A decision based on EMV indicates not insuring is optimal. But what if the farmer is uncertain about own priors (subjective) beliefs (probabilities)? What if a forecast is obtainable for disease outbreaks?

Accounting for new information

› Usually, we are presented with situations in which the initial information about uncertain events is incomplete and we might be able to gather more information:

– Purposeful experimentation, obtaining forecasts, recording more events as they occur

– How should we revise our prior probabilities to account for new information?

Probability updating with Bayes’ theorem

› Often called Bayesian Inference

– A standard method for updating probabilities as information is acquired

› New information may be summarised as a new set of probabilities – Say, data from an experiment

– These data may be used to make some projections of future outcomes

Probability updating with Bayes’ theorem

Bayes’ theorem

Example: Foot and mouth disease [HHA2004 pp.25]

› Continuation of example from earlier in book, which involved the farmer making a choice of whether or not to take out insurance against losses related to FMD outbreak

› Let’s say the farmer initially believes the probabilities are: – Outbreak: 6%

– No outbreak: 94%

› These are called prior probabilities

– That is, those elicited before subsequent information is acquired

Example: Foot and mouth disease [HHA2004 pp.25]

Example: Foot and mouth disease [HHA2004 pp.25]

› The accuracy of the group’s predictions can be judged by evaluating past performance of predictions against actual events

› These are (Zk|Si):

Example: Likelihood probabilities

Example: Probability tree

Example: Joint probabilities

Example: Joint probabilities

Likelihood Joint

Example: Marginal probabilities

Example: Posterior probabilities

Example: ‘Flipped’ probability tree

Example: ‘Flipped’ probability tree

Example: ‘Flipped’ probability tree

Example: ‘Flipped’ probability tree

We really care about these probabilities

Example: Posterior probabilities

Example: Posterior probabilities

Event | Prediction

Marginal probability

Joint probability

Posterior probability

Example: Posterior probabilities

Bayesian updating process

Bayesian updating process

When the forecast is made-comparison

Subjective probabilities

Posterior Probs – outbreak possible

don’t insure

don’t insure

Posterior Probs – outbreak unlikely

don’t insure

P(S|Z ) P(Si)i 1

Posterior Probs – outbreak probable

don’t insure

P(PS(S) |Z ) ii2

P(S|Z ) ii3

What drives these results?

Comparison (using CE values from last week’s lecture)

forecast unlikely

Subjective probabilities

Posterior Probs – outbreak unlikely

don’t insure

don’t insure

ak0.989474

forecast possible

forecast probable

Posterior Probs – outbreak possible

Posterior Probs – outbreak probable

P(S|Z ) P(Si)i 2

don’t insure

P(S) P(Si i|Z3)

don’t insure

ak0.921569

ak0.758065

What drives these results?

› If a forecast that the outbreak is unlikely, don’t insure.

› If a forecast that the outbreak is possible or probable, insure.

› Although priors are strong, results driven by the accuracy of the forecast tool- likelihood probabilities.

› We can used these revised probabilities in decision making analysis.

› We can also determine a value of incorporating this information. How?

– Essentially calculate the expected value/utility of the problem before incorporating the information (ie the problem based on prior probabilities). Then, the value of the information is the difference between this value/utility amount and the amount of expected value/utility from an optimum strategy that following from incorporating the information. If this is positive, the forecast is worth buying at a cost up to the value/utility of this difference in terms of $.

– NB if calculated in terms of utility then it is necessary to back transform the utility value to $ amount.

Computation of forecast value

› Expected value before the forecast= $493.04K (1)

› Expected value with forecast, need to incorporate the probabilities of

getting the forecasts (P(Zi)):

› P(Z1)*489.7789+P(Z2)*492.8+P(Z3)*492.8

› =0.57*489.7789+0.306*492.8+0.124*492.8

› =$496.208K (2)

› Expected value from incorporating forecast information: (2)-(1)=

› =$496.208K -$493.04K = $3.168K

› This value is an upper bound on what the DM should be prepared to pay for the forecast.

› [HHA2004] Hardaker, Huirne and Anderson (2004) Coping with Risk in Agriculture, CAB International.

– Chapter 3, ‘Accounting for new information’, at the end of the chapter

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