# x

** Elements of the decision prob**: Decisions to make; Uncertain
events; Value of specific outcomes/

**: graphical representation of uncertain quantities and decisions that explicitly reveals probabilistic dependence and the flow of information/**

*Influence Diagrams***: Decision: information flow& the chronological order. Arcsvalue&chance: conditional and show probabilistic dependence between decision elements. A->B: B is conditioned on the value of A/**

*Arcs***: relative impact of different variables/ explore the impact of changes in Ps on decision/ Two-way: 2 variables at the same time/Tornado: Length of bar: sensitive/ importance of each variable/ Spider: percentage deviation from base case vs expected NPV/**

*Sensitivity analysis***: Expected return-a measure of central tendency/ Variance-an average deviation measure of dispersion, obtained by averaging the squares of deviations of individual observations from the mean/ SemiVar-by minimizing standard deviation, the optimization penalize projects with upside and mainly downside/ Normal distribution-mean=mode=median/ Lognormal distri-skew to one side, straight line with cumulative frequency/ Uniform distri-only specify a min and a max/ Triangular distri- estimate the min, most likely and max/**

*Risk and return***-Event A and B are independent if and only if: P(A)=P(A|B)=P(A n B)/P(B), P(A,B)=P(A)P(B)/ Conditional independence-A and B: conditionally independent=>P(A n B|C)=P(A|C)P(B|C)/ Marginal Event-union, unconditional/ Joint Event-intersection/ Conditional prob-P(A,B)=P(B)P(A|B)/**

*Independent event***: Prior Prob+New Info+B.T=>Posterior Prob(Revised Prob) /**

*Bayes Theorem***-Info only has value in a decision problem if it results in a change in some action to be taken by a DM/ Perfect Info-perfectly reliable, EVPI=EV-EV w/o info/ Value of Imperfect Info-EVSI=EV w/ sample info-EV w/o info**

*Value of information*** Information can add value along multiple dimension**: cost: avoid
non-commercial prospects,less wells needed for field appraisal,fewer dry
holes,better field development,avoid overcapacity in field development. reservoir value:select
the best prospect in a ranking process,make sure topside facilities have
sufficient capacity, optimize production and recovery. uncertainty:success
rates, reservoir areal extent, compartmentalization,reserve size, improve
confidence in estimates/

**: probability of x successes in n independent trials= n:number of independent trials, x: number of successes in the n trials, p: probability od success on any given trial, : combination of n things taken x at a time/**

*Binomial approach***: objective: define the distribution of outcomes which could be anticipated for the project. Considers the impact of changes on all variables simultaneously.**

*Simulation***: /**

*Covariance***: coefficient of determination: the fraction of the variability in the returns on the one investment that can be associated with variability in the returns on the other.**

*Correlation coefficient***: 1.Capability to define uncertainty as a range and distribution of possible outcomes for each factor; 2.May be applied to any type of non-deterministic analysis; 3.No limit to the number of variables that may be modeled; 4.distributions of random variables can be of any type; 5.Integrates both above-ground and below-ground risks into decision process; 6.Different individuals can describe uncertainty about different components of the problems; 7.Lends itself well to sensitivity analysis; 8.Provides valuable inputs to decision tree modeling/**

*Advantages to simulation***: Compare outcomes, x轴. Conditions: 1.One alternative dominantes the other with certainty; 2.Probability density functions do not intersect.**

*Deterministic dominance***: compare probability, y轴. Conditions: 1. For all values in the outcome set, alternative A is more likely to exceed that value than alternative B; 2.When the probability density functions do cross and the cumulative probability distributions of competing alternatives do not cross/**

*Probabilistic/stochastic dominance***/**

*Risk and return:***: the indicator of the degree to which a stock responds to changes in the return produced by the market. /**

*Beta***: 1.Orderability&transitivity; 2.Reduction of compound uncertain events概率相乘相加简化; 3.Continuity/Independence; 4.Substitutability; 5.Monotonicity; 6.Invariance; 7.Finitness**

*Expected utility axioms**Limitations of
Expected Value Analysis**:* 1. The firm doesn’t possess an
unlimited pool of exploration capital; 2.The Firm is Not Risk Neutral; 3.EMV
Fails to Provide Guidance on Limiting the Downside Exposure. EMV does not
Consider the Magnitude of Money Exposed to the Chance of Loss/ **Condition for Risk Neutrality**:
Firm must be Impartial to the Magnitudes of Potential Profits and Losses/ **Preference or Expected Utility Theory**:1.*Dominant approach to the
theory of decision making in both economics and finance; 2.Establishes the
process of modeling an individual or firm’s risk propensity; 3.Enables decision
maker to incorporate risk attitudes into the decision process; 4.Provides the
firm a technique for determining the appropriate level of diversification/ ***Certainty Equivalent**: That
certain value for an uncertain event which a decision maker is just willing to
accept in lieu of the gamble represented by the event/ **Risk neutral behavior** is reflected by a straight line;
maximizing EV is equivalent to maximizing EU/ **Risk averse behavior** is reflected by a concave utility
function; in this case, the CEQ is less than the expected value of the payoff/ **Risk seeking behavior** is
reflected by a convex utility function; it is the opposite of risk aversion in
that the CEQ for a gamble is greater than the expected value of the payoff /**CEQ, expected value, and risk premium
all depend on two factors**: The decision maker’s or firm’s utility
function;The probability distribution of payoffs/ **Expected Utility Axioms**:Orderability and Transitivity;Reduction
of Compound Uncertain Events; Continuity or Independence; Substitutability (The
“Do you really mean it?” axiom);Monotonicity; Invariance; Finiteness. /**This utility function has two important
properties**: The utility of any lottery is the expected utility of its
prizes; If the decision maker prefers one lottery to another, then it must have
the higher utility.* (*If the attribute of interest is such that more is
always better, then the utility curve will always be monotonically increasing.)/
**Decreasing Risk Aversion**: Condition
which implies that the degree of risk aversion decreases as the payoffs
increase. The decreasing risk premium reflects decreasing risk aversion,
which is a property of the logarithmic form of utility function/ **When constant risk aversion holds and
events are independent**, multiple projects can be treated separately. The
sum of the CEQs for independent projects is equal to the CEQ of the portfolio
of projects/ **Exponential Utility
Function**:*U(x) = a – be ^{-x/R}*;
/

**Risk Tolerance (R)**: value represents the sum of money at which the decision makers are indifferent as a company investment to a 50-50 chance of winning that sum and losing half that sum. It captures in monetary terms the notion of assessing tradeoffs between potential upside gains versus downside losses/

**Risk-sharing Pareto-optimal**: Allocation in which no one firm can be made better off without the other firm being made worse off/

**Linear Sharing Rule**: When two individuals have exponential utility functions, then they take proportional shares in the ratio of RT1 to RT2

**Measuring Risk Tolerance**: Surveys & Interviews