目標 : {350 250} 85 {8,000 .. 60万} 毎月 유지
Importance: 5/5
Compound growth, present/future value, annuities, inflation, retirement income
An Introduction to the Mathematics of Finance
Authors: Stephen Garrett
Edition: 2nd
Publisher: Elsevier/Butterworth-Heinemann
Strong foundation for retirement accumulation, annuities, discounting, and cash-flow mathematics.
Importance: 5/5
Uncertain returns, longevity, income shocks, Monte Carlo simulation
A First Course in Probability
Authors: Sheldon Ross
Edition: 10th
Publisher: Pearson
Builds the probability foundation needed for random investment returns, lifespan uncertainty, and simulation.
Importance: 5/5
Estimation, confidence intervals, hypothesis testing, strategy comparison
Statistical Inference
Authors: George Casella; Roger L. Berger
Edition: 2nd
Publisher: Duxbury
Rigorous foundation for estimation, likelihood, hypothesis testing, and inference used in empirical thesis work.
Importance: 5/5
Measure relationships among salary, taxes, contributions, and retirement wealth
Applied Linear Statistical Models
Authors: Michael H. Kutner; Christopher J. Nachtsheim; John Neter; William Li
Edition: 5th
Publisher: McGraw-Hill
Useful for modeling how salary, tax variables, contribution choices, and demographics relate to retirement outcomes.
Importance: 4/5
Sensitivity of wealth to multiple changing variables
Calculus: Early Transcendentals
Authors: James Stewart; Daniel Clegg; Saleem Watson
Edition: 9th
Publisher: Cengage
Review gradients, partial derivatives, constrained extrema, and multivariable optimization concepts.
Importance: 4/5
Regression, covariance matrices, simulations, numerical computation
Linear Algebra and Its Applications
Authors: David C. Lay; Steven R. Lay; Judi J. McDonald
Edition: 6th Global
Publisher: Pearson
Essential for regression, matrix computations, covariance structures, and computational statistics.
Importance: 5/5
Find contribution and tax strategies maximizing after-tax retirement wealth
Introduction to Operations Research
Authors: Frederick S. Hillier; Gerald J. Lieberman
Edition: 11th
Publisher: McGraw-Hill
Covers constrained optimization and decision models useful for contribution limits, tax constraints, and retirement strategy selection.
Importance: 4/5
Solve models without convenient closed-form solutions
Numerical Analysis
Authors: Richard L. Burden; J. Douglas Faires; Annette M. Burden
Edition: 10th
Publisher: Cengage
Useful for root-finding, approximation, numerical integration, and solving computational retirement models.
Importance: 4/5
Historical returns, inflation, wage growth, and economic variables
Time Series Analysis
Authors: James D. Hamilton
Edition: 1st
Publisher: Princeton University Press
Classic graduate reference for modeling economic and financial variables across time.
Importance: 5/5
Connect mathematical models to real teacher, salary, pension, and economic data
Introductory Econometrics: A Modern Approach
Authors: Jeffrey M. Wooldridge
Edition: 8th
Publisher: Cengage
Excellent bridge from regression to causal and panel-data analysis for teacher and district datasets.
Importance: 5/5
Model investment returns, inflation, salary growth, and wealth paths
Introduction to Probability Models
Authors: Sheldon M. Ross
Edition: 13th
Publisher: Academic Press / Elsevier
Core reference for Markov chains, Poisson processes, renewal theory, and other stochastic models applicable to lifetime wealth paths.
Importance: 5/5
Generate and analyze 10,000–100,000+ retirement scenarios
Monte Carlo Statistical Methods
Authors: Christian P. Robert; George Casella
Edition: 2nd
Publisher: Springer
Advanced reference for simulation, random sampling, variance reduction, and Monte Carlo inference.
Importance: 4/5
Optimize decisions subject to IRS, pension, income, and contribution constraints
Introduction to Operations Research
Authors: Frederick S. Hillier; Gerald J. Lieberman
Edition: 11th
Publisher: McGraw-Hill
Provides linear, nonlinear, network, and decision optimization tools for constrained retirement planning models.
Importance: 5/5
Determine optimal decisions at each age based on future consequences
Dynamic Programming and Optimal Control, Vol. I
Authors: Dimitri P. Bertsekas
Edition: 4th
Publisher: Athena Scientific
Directly applicable to sequential lifetime decisions such as Roth vs. traditional contributions, conversion timing, and withdrawals.
Importance: 4/5
Longevity, annuities, pensions, and retirement-period risk
Actuarial Mathematics for Life Contingent Risks
Authors: David C. M. Dickson; Mary R. Hardy; Howard R. Waters
Edition: 3rd
Publisher: Cambridge University Press
Useful for survival probabilities, life annuities, pensions, longevity risk, and actuarial valuation.
Importance: 5/5
Translate tax rules, salary schedules, pensions, and investment choices into equations
A First Course in Mathematical Modeling
Authors: Frank R. Giordano; William P. Fox; Steven B. Horton
Edition: 5th
Publisher: Cengage
Helps convert real retirement-planning rules and institutional constraints into tractable mathematical models.