Roger B. Myerson - Probability Models for Economic Decisions (The MIT Press)

1. 4.3Lognormal Distributions
2. 8.6Fundamental Ideas of Arbitrage Pricing Theory

List of Figures

Simulation of coin tossing in a spreadsheet

Coin tossing with adjustable probabilities

Simple model of independent sales calls

Model of 20 sales calls with uncertainty about salespersons skill

Simulation table for model of 20 sales calls

Simulation data and analysis

Data table of results for different numbers of sales

Frequencies of sales in simulation data (total and by skill level)

Sales model with skill level from a Triangular distribution

Simulation model of oil-exploration example

Probability tree for oil-exploration example

Alternative tree and model for oil-exploration example

Binomial probability computations for salesperson example

Computing frequencies of different outcomes in oil-exploration example

Five stages of the modeling process

Discrete probability distribution for the number of entrants (K)

Inverse cumulative-probability curve for number of entrants (K)

Simulation with a discrete probability distribution (four equivalent formulas)

Making a simple simulation model of competitors and profit

Expected values and standard deviations of discrete random variables

Estimating an expected value and standard deviation from simulation data

Estimate of an inverse cumulative distribution from simulation data

A spreadsheet for studying the properties of a sample mean

Analysis of the Superior Semiconductor case

Cumulative risk profile from simulation data

A simulation model with three random variables affecting profit

Utility function with constant risk tolerance for Superior Semiconductor (part B)

Analysis of Superior Semiconductor (part B) with constant risk tolerance

Estimating local risk tolerances with constant or linear risk tolerance

A spreadsheet illustrating the derivation of utility theory

Derivation of exponential utility from constant risk tolerance

The Normal distribution

Compound interest and growth rate calculations with EXP and LN

The multiplication and addition properties of EXP and LN

Repeated investment strategies yielding payoffs that are approximately Normal or Lognormal

Repeated investment strategies over the short, medium, and long term

Annualized returns by investment horizon

Total returns by investment horizon

Subjectively assessed quartiles and a Generalized Lognormal distribution

Simulation analysis of the Superior Semiconductor (part C) case

Certainty equivalent of a Normal lottery

Comparison of Lognormal, Gamma, and Normal distributions

Joint probability distribution of two random variables

Correlation of two discrete random variables and portfolio analysis

Price data and annual growth ratios in the 1980s for six mutual funds

Computing the correlation of Funds 1 and 2

Making a model of the annual growth ratios of six funds

Extending historical data by simulation

Simulations with independent funds

Portfolio calculations for investments in the six funds

A simple example where Solver can fail

Probabilistic electoral forecasting in one state

Probabilistic electoral forecasting in 50 states

Distribution of electoral votes

Ignoring the effects of uncertainty

Ignoring the effects of correlation in the forecasting errors across states

Computing conditional medians for subjective correlation assessment

Non-Normal random variables and normalized rank correlations

Making Multivariate Normal random variables

Conditional expected skills, given sales results, from a Beta prior

Prior and posterior inverse cumulative distributions for salespersons skill

Conditional probability and conditional expectation in a discrete example

Backwards analysis of conditional expectations in a tree diagram

An example of dependence among random variables with correlation 0

Modeling uncertainty about a probability

Estimating a linear regression relationship among random variables

A simulation with 100 trials of

Visual display of our estimates of the relationship between two random variables

Minimizing squared errors of linear estimates in regression analysis

Simulation analysis of one production quantity in the Scotia case

Simulation analysis of four alternative production quantities in the Scotia case

A spreadsheet for finding the optimum among all possible production quantities for Scotia

Strategic value of information about weather in the Scotia case

Conditional expected profits, given weather, for Scotias optimal strategies

Tree diagram for Scotias decision without forecast information

Tree diagram for Scotias decision with forecast information

Optimal overbooking in a revenue management problem

Revenues, profits, and unused capacity

Model of bidding to sell in the Bates case, part A (no winners curse)

Finding optimal bids for the Bates case, part A (no winners curse)

Bidding to buy a lemon

Bidding model for the Bates case, part B (with winners curse)

Inverse cumulative distribution for the opposing bid-to-beat in Bates (part B)

Finding optimal bids for the Bates case, part B (with winners curse)

Alphas bidding for Valdez, when others bid 80% of their estimated values

Alphas bidding for Valdez, when others bid 60% of their estimated values

Game model of bidding for Valdez

Sharing a Normal gamble

Optimal risk sharing among three partners with constant risk tolerance

A spreadsheet to evaluate nonlinear sharing rules

Optimal risk sharing in a discrete example

Optimal risk sharing with moral hazard in a discrete example

Optimal linear incentive plan for an agent with moral hazard

Optimal piecewise-linear incentive plan for an agent with moral hazard

Comparing investments that differ in correlation with the market portfolio

Computing an assets value in a market with constant risk-tolerant investors