1.
Actuarial science
–
Actuarial science is the discipline that applies mathematical and statistical methods to assess risk in insurance, finance and other industries and professions. Actuaries are professionals who are qualified in this field through intense education, in many countries, actuaries must demonstrate their competence by passing a series of thorough professional examinations. Actuarial science includes a number of interrelated subjects, including mathematics, probability theory, statistics, finance, economics, historically, actuarial science used deterministic models in the construction of tables and premiums. The science has gone through changes during the last 30 years due to the proliferation of high speed computers. Many universities have undergraduate and graduate programs in actuarial science. In 2010, a study published by job search website CareerCast ranked actuary as the #1 job in the United States, the study used five key criteria to rank jobs, environment, income, employment outlook, physical demands, and stress. A similar study by U. S. News & World Report in 2006 included actuaries among the 25 Best Professions that it expects will be in demand in the future. Actuarial science became a mathematical discipline in the late 17th century with the increased demand for long-term insurance coverage such as Burial, Life insurance. These long term coverage required that money be set aside to pay future benefits, such as annuity and this led to the development of an important actuarial concept, referred to as the Present value of a future sum. Certain aspects of the methods for discounting pension funds have come under criticism from modern financial economics. Contemporary life insurance programs have extended to include credit and mortgage insurance, key man insurance for small businesses, long term care insurance. The effects of consumer choice and the distribution of the utilization of medical services and procedures. These factors underlay the development of the Resource-Base Relative Value Scale at Harvard in a multi-disciplined study, actuarial science also aids in the design of benefit structures, reimbursement standards, and the effects of proposed government standards on the cost of healthcare. It is common with mergers and acquisitions that several pension plans have to be combined or at least administered on an equitable basis, benefit plans liabilities have to be properly valued, reflecting both earned benefits for past service, and the benefits for future service. Actuarial science is applied to Property, Casualty, Liability. In these forms of insurance, coverage is provided on a renewable period. Coverage can be cancelled at the end of the period by either party, Property and casualty insurance companies tend to specialize because of the complexity and diversity of risks. One division is to organize around personal and commercial lines of insurance, personal lines of insurance are for individuals and include fire, auto, homeowners, theft and umbrella coverages

2.
100-year flood
–
A one-hundred-year flood is a flood event that has a 1% probability of occurring in any given year. The 100-year flood is also referred to as the 1% flood, for river systems, the 100-year flood is generally expressed as a flowrate. Based on the expected 100-year flood flow rate, the water level can be mapped as an area of inundation. The resulting floodplain map is referred to as the 100-year floodplain, estimates of the 100-year flood flowrate and other streamflow statistics for any stream in the United States are available. Maps of the riverine or coastal 100-year floodplain may figure importantly in building permits, environmental regulations, a common misunderstanding exists that a 100-year flood is likely to occur only once in a 100-year period. In fact, there is approximately a 63. 4% chance of one or more 100-year floods occurring in any 100-year period, on the Danube River at Passau, Germany, the actual intervals between 100-year floods during 1501 to 2013 ranged from 37 to 192 years. The probability of exceedance Pe is also described as the natural, inherent, however, the expected value of the number of 100-year floods occurring in any 100-year period is 1. Ten-year floods have a 10% chance of occurring in any year, 500-year have a 0. 2% chance of occurring in any given year. The percent chance of an X-year flood occurring in a year can be calculated by dividing 100 by X. A similar analysis is applied to coastal flooding or rainfall data. The recurrence interval of a storm is rarely identical to that of a riverine flood, because of rainfall timing. The field of value theory was created to model rare events such as 100-year floods for the purposes of civil engineering. This theory is most commonly applied to the maximum or minimum observed stream flows of a given river, in desert areas where there are only ephemeral washes, this method is applied to the maximum observed rainfall over a given period of time. The extreme value analysis only considers the most extreme event observed in a given year. So, between the spring runoff and a heavy summer rain storm, whichever resulted in more runoff would be considered the extreme event. There are a number of assumptions which are made to complete the analysis determines the 100-year flood. First, the events observed in each year must be independent from year-to-year. In other words, the river flow rate from 1984 cannot be found to be significantly correlated with the observed flow rate in 1985

3.
Actuarial notation
–
Actuarial notation is a shorthand method to allow actuaries to record mathematical formulas that deal with interest rates and life tables. Traditional notation uses a system where symbols are placed as superscript or subscript before or after the main letter. Example notation using the system can be seen below. Various proposals have made to adopt a linear system where all the notation would be on a single line without the use of superscripts or subscripts. Such a method would be useful for computing where representation of the system can be extremely difficult. However, a linear system has yet to emerge. I is the effective interest rate, which is the true rate of interest over a year. Thus if the annual interest rate is 12% then i =0.12, I is the nominal interest rate convertible m times a year, and is numerically equal to m times the effective rate of interest over one m th of a year. For example, i is the rate of interest convertible semiannually. If the effective rate of interest is 12%, then i /2 represents the effective interest rate every six months. Since 2 =1.12, we have i /2 =0.0583, the appearing in the symbol i is not an exponent. It merely represents the number of interest conversions, or compounding times, semi-annual compounding, is frequently used in valuing bonds and similar monetary financial liability instruments, whereas home mortgages frequently convert interest monthly. Following the above example again where i =0.12, effective and nominal rates of interest are not the same because interest paid in earlier measurement periods earns interest in later measurement periods, this is called compound interest. That is, nominal rates of interest credit interest to an investor, the result is more frequent compounding of interest income to the investor, when nominal rates are used. For example, if you need 1 in one year, then the amount of money you should invest now is,1 × v, if you need 25 in 5 years the amount of money you should invest now is,25 × v 5. By contrast, an effective rate of interest is calculated by dividing the amount of interest earned during a one-year period by the balance of money at the beginning of the year. The present value of a payment of 1 that is to be made n years in the future is n and this is analogous to the formula n for the future value n years in the future of an amount of 1 invested today. D, the rate of discount convertible m times a year, is analogous to i