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In Section 11 of his Mathematical Economics Problems and Solutions, Mr. Stolyarov presents detailed answers to four problems regarding expected utility and its relationship to concepts such as insurance and indifference curves.

Section 10 of Mr. Stolyarov's Mathematical Economics Problems and Solutions gives solutions to four problems involving the use of second order conditions in functions with two choice variables.

Mr. Stolyarov gives ten practice problems and solutions regarding issues in fiscal and monetary stabilization policy, the Phillips Curve model, Milton Friedman's objections to stabilization policy, time inconsistency, policy lags, and related concepts.

Section 10 of Mr. Stolyarov's Intermediate Macroeconomics Problems and Solutions discusses concepts related to monetary policy, the credit channel, and the Aggregate Supply / Aggregate Demand model. Solution to all problems are provided.

Section 12 of Mr. Stolyarov's Intermediate Macroeconomics Problems and Solutions focuses on a diversity simple mathematical and conceptual views of economic growth -- including the theories of Malthus and Cobb-Douglas production functions.

Section 13 of Mr. Stolyarov's Intermediate Macroeconomics Problems and Solutions gives 5 practice questions regarding the relationship among capital, investment, and economic growth from the standpoint of various economic models.

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Mr. Stolyarov presents solutions to two combinatorics problems regarding the partitions of integers.

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Section 14 of Mr. Stolyarov's Intermediate Macroeconomics Problems and Solutions includes eight multiple-choice questions regarding exogenous and endogenous economic growth models, including the Solow growth model. Solutions are provided.

Section 9 of Mr. Stolyarov's Intermediate Macroeconomics Problems and Solutions addresses common features of today's banking system and the Federal Reserve's involvement with it. Answers to the questions are provided.

Section 12 of Mr. Stolyarov's Mathematical Economics Problems and Solutions explores contracts that can be designed under conditions of asymmetric information to give managers incentives to work hard. This section concerns ways to get around the principal-agent problem.

Mr. Stolyarov presents mathematical problems and solutions regarding the economics of fisheries -- including problems pertaining to the logistic population growth model, the Schaefer model, and the Gordon model.

Mr. Stolyarov presents 5 practice problems pertaining to Robert Deacon's model of forest economics and the benefits and costs of harvesting a forest. Solutions are provided. This section is recommended for students of mathematical economics.

Mr. Stolyarov presents four practice problems and solutions involving constrained optimization using the Lagrangian method. This section is highly recommended for students of mathematical economics.

Section 8 of Mr. Stolyarov's Intermediate Macroeconomics Problems and Solutions includes five questions on the workings of the Federal Reserve system. Answers are provided.

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In Section 3 of his Intermediate Macroeconomics Problems and Solutions, Mr. Stolyarov presents the equation for the quantity theory of money and five practice problems and solutions regarding it.

Section 2 of Mr. Stolyarov's Intermediate Macroeconomics Problems and Solutions offers five conceptual multiple-choice questions on the underpinnings of the classical gold standard. This section is recommended for students of intermediate macroeconomics.

Mr. Stolyarov presents five conceptual questions and solutions regarding the Aggregate Supply / Aggregate Demand (AS-AD) model and several other macroeconomic models. This section is suited for students of intermediate macroeconomics.

Mr. Stolyarov gives five practice problems and solutions on the concepts and formula for the money multiplier. These questions are particularly suitable for intermediate macroeconomics students.

Mr. Stolyarov presents five intermediate macroeconomics problems and solutions on concepts pertaining to business cycles.

In Section 4 of his Intermediate Macroeconomics Problems and Solutions, Mr. Stolyarov presents five conceptual multiple-choice questions relating to money and inflation. Solutions are provided.

Section 21 of The Actuary's Free Study Guide for Exam 3F / Exam MFE gives 5 practice problems and solutions for how to apply the binomial option pricing model to options on currencies.

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Section 22 of The Actuary's Free Study Guide for Exam 3F / Exam MFE gives formulas and practice problems and solutions for finding the prices of options on futures contracts using the binomial model.

Section 20 of The Actuary's Free Study Guide for Exam 3F / Exam MFE discusses how to use the binomial option pricing model to determine the prices of American call and put options. 5 sample problems and solutions are provided.

Section 33 of The Actuary's Free Study Guide for Exam 3F / Exam MFE introduces the Black-Scholes formula for option pricing, its assumptions, its components, and 5 practice problems and solutions.

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Section 19 of The Actuary's Free Study Guide for Exam 3F / Exam MFE discusses an approach toward binomial option pricing of put options and presents 5 original practice problems and solutions. As a special bonus, an extremely useful time-saving formula is introduced.

Section 31 of The Actuary's Free Study Guide for Exam 3F / Exam MFE gives 5 practice problems and solutions regarding Schroder's method for constructing binomial stock price trees when the stock pays discrete dividends.

Section 30 of The Actuary's Free Study Guide for Exam 3F / Exam MFE discusses alternative approaches to constructing binomial trees - including the Cox-Rubinstein binomial tree and the lognormal tree. 5 practice problems and solutions are given.

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Mr. Stolyarov presents the equations for put-call parity and gives five original sample problems and solutions using which actuaries can internalize the concepts involved. This section is particularly suited to studying for Exam 2 / Exam FM and Exam 3F / Exam MFE.

Mr. Stolyarov discusses how the same option can be a call or put depending on our choice of underlying asset and strike asset. He presents problems and solutions relating to classifying options as calls or puts -- especially in the context of currency options.

Mr. Stolyarov discusses the formula for parity of options on bonds and presents five original practice problems and solutions in this 5th section of The Actuary's Free Study Guide for Exam 3F / Exam MFE.

Mr. Stolyarov presents the formula for put-call parity on currency options and offers five practice problems and solutions for actuaries preparing for Exam 3F / Exam MFE.

Section 34 of The Actuary's Free Study Guide for Exam 3F / Exam MFE presents a variant of the Black-Scholes option pricing formula that uses prepaid forward prices on the underlying asset and the strike asset. 5 practice problems and solutions are given.

This section of The Actuary's Free Study Guide for Exam 3F / Exam MFE discusses the boundaries and constraints on prices of American and European call options and presents five original problems and solutions on this topic.

This section of The Actuary's Free Study Guide for Exam 3F / Exam MFE discusses when it is never optimal to exercise American put and call options early and when such exercise might be optimal. Practice problems and solutions are provided.

Section 17 of The Actuary's Free Study Guide for Exam 3F / Exam MFE explores a method of constructing binomial trees in the one-period binomial option pricing model. It includes 5 practice problems and solutions

In Section 12 of The Actuary's Free Study Guide for Exam 3F / Exam MFE, the concept of strike price convexity is discussed and sample problems and solutions are presented.

This section of The Actuary's Free Study Guide for Exam 3F / Exam MFE describes the various relationships among prices of options with different strike prices. 5 practice problems and solutions are included.

This section of The Actuary's Free Study Guide for Exam 3F / Exam MFE discusses how time to expiration affects the prices of European and American call and put options. Five practice problems and solutions are provided.

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The delta-gamma approximation is used to estimate option price movements if the underlying stock price changes. Section 47 of The Actuary's Free Study Guide for Exam 3F / Exam MFE gives 5 practice problems and solutions regarding this approximation.

Section 52 of The Actuary's Free Study Guide for Exam 3F / Exam MFE presents the eight different types of Asian options, formulas for calculating arithmetic and geometric averages, and 5 practice problems and solutions.

Section 53 of The Actuary's Free Study Guide for Exam 3F / Exam MFE explains the various kinds of barrier options available and gives five practice problems and solutions regarding them.

Section 50 of The Actuary's Free Study Guide for Exam 3F / Exam MFE presents formulas for the return and the variance of the return to a delta-hedged market-maker. 5 practice problems and solutions are available.

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Section 49 of The Actuary's Free Study Guide for Exam 3F / Exam MFE presents the Black-Scholes partial differential equation relation option price to the values of the option Greeks. 5 practice problems and solutions are given.

Section 56 of The Actuary's Free Study Guide for Exam 3F / Exam MFE addresses gap options -- options for which the trigger price and strike price are different. 5 practice problems and solutions about pricing these options are available.

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Section 62 of The Actuary's Free Study Guide for Exam 3F / Exam MFE presents the statement of Ito's Lemma as applicable to arithmetic, mean-reversion, and geometric Brownian motion. 5 practice problems and solutions are available.

Section 61 of The Actuary's Free Study Guide for Exam 3F / Exam MFE gives an introduction to mean reversion processes in Brownian motion -- including the Ornstein-Uhlenbeck process. 5 practice problems and solutions are provided.

Section 60 of The Actuary's Free Study Guide for Exam 3F / Exam MFE continues to introduce students to Brownian motion, this time focusing on geometric Brownian motion and basic applications. 5 problems and solutions are available.

Mr. Stolyarov presents a revised version of Section 49 of The Actuary's Free Study Guide for Exam 3F / Exam MFE. The correct formula is now given, with proper adjustments made to the five practice problems and solutions.

Mr. Stolyarov presents and solves several optimization problems in mathematical economics, where the objective function is subject to multiple inequality constraints. Graphical illustrations are provided.

Section 48 of The Actuary's Free Study Guide for Exam 3F / Exam MFE gives 5 practice problems and solutions on the delta-gamma-theta approximation for changes in option prices and market-maker profits.

Section 40 of The Actuary's Free Study Guide for Exam 3F / Exam MFE presents the option Greeks gamma and vega and 5 practice problems and solutions to help actuarial students and other interested individuals learn these measures.

Section 41 of The Actuary's Free Study Guide for Exam 3F / Exam MFE introduces the option Greeks theta, rho, and psi, as well as a formula for obtaining the Greek measures for entire portfolios consisting of various options. 5 practice problems and solutions are given.

Section 39 of The Actuary's Free Study Guide for Exam 3F / Exam MFE gives five practice problems and solutions regarding the option Greek delta, which measures the option price change when the stock price increases by $1.

Section 37 of The Actuary's Free Study Guide for Exam 3F / Exam MFE presents the Black formula for pricing European options on a futures contract and 5 practice problems and solutions regarding it.

The Garman-Kohlhagen Formula is a variant on the Black-Scholes option pricing formula, applied to finding the prices of currency options. Section 36 of The Actuary's Free Study Guide for Exam 3F / Exam MFE gives 5 practice problems and solutions regarding it.

Section 42 of The Actuary's Free Study Guide for Exam 3F / Exam MFE presents the concepts of option elasticity and option price volatility and 5 practice problems and solutions regarding them.

Section 43 of The Actuary's Free Study Guide for Exam 3F / Exam MFE gives formulas for the risk premium and Sharpe ratio of an option, along with 5 practice problems and solutions to help actuarial students.

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Section 45 of The Actuary's Free Study Guide for Exam 3F / Exam MFE presents the concepts of calendar spreads and implied volatility and 5 practice problems and solutions regarding them.

Section 44 of The Actuary's Free Study Guide for Exam 3F / Exam MFE gives formulas for the elasticity and risk premiums of call option portfolios consisting of options on the same underlying asset. 5 practice problems and solutions are provided.

Section 35 of The Actuary's Free Study Guide for Exam 3F / Exam MFE discusses option pricing using the Black-Scholes formula when the underlying stock pays discrete dividends. 5 practice problems and solutions are given.

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Many commercial cleansers contain harmful substances that can release toxic fumes in your home. Others can burn your skin or cause allergic reactions. Check out these five non-toxic cleaning solutions and make your Spring Cleaning a healthy endeavor!

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