# Monthly Archives: 2013年四月

## Technology and Invention in Finance

##### Overview:

Technology and innovation underlie finance. In order to manage risks successfully, particularly long-term, we must pool large amounts of risk among many, diverse people and overcome barriers such as moral hazard and erroneous framing. Inventions such as insurance contracts and social security, and information technology all the way from such simple things as paper, and the postal service to modern computers have helped to manage risks and to encourage financial systems to address issues pertaining to risk. The tax and welfare system is one of the most important risk management systems.

## The Universal Principle of Risk Management: Pooling and the Hedging of Risks

##### Overview:

Statistics and mathematics underlie the theories of finance. Probability Theory and various distribution types are important to understanding finance. Risk management, for instance, depends on tools such as variance, standard deviation, correlation, and regression analysis. Financial analysis methods such as present values and valuing streams of payments are fundamental to understanding the time value of money and have been in practice for centuries.

Probability P, 0<P<1
• Multiplication rule for independent events: Prob(A and B) = Prob(A)*Prob(B)
• Probability of n independent accidents = P^n
• Probability of x accidents in n policies (Binomial Distributon):

Expected Value, Mean, Average

Variance and Standard Deviation

• Variance (^2)is a measure of dispersion
• Standard deviation is square root of variance

Covariance
• A Measure of how much two variables move together

Correlation
• A scaled measure of how much two variables move together

Present Discounted Value (PDV)
• PDV of a dollar in one year = 1/(1+r)
• PDV of a dollar in n years = 1/(1+r)^n
• PDV of a stream of payments x1,..,xn

Consol and Annuity Formulas
• Consol pays constant quantity x forever
• Growing consol pays x(1+g)^(t-1) in t
• Annuity pays x from time 1 to T