SOA Exams & Modules
Developing an ERM Framework ERM Framework Criteria (Effective ) Scope is enterprise-wide All risk categories included Focused on key risks Enhances decision making ability Integration across risk type Aggregated metrics Balanced risk & return management Appropriate disclosures Measures value impacts Primary stakeholder focus Challenges to ERM Analysis The implementation of a strong ERM framework must address three primary hurdles. Quantification …
[mathjax] Introduction The Introduction to ILA module will give an overview of the role of an actuary in a Life and Annuity context. The module will give a strong foundation of understanding of life insurance and annuity product features, markets and distribution. Candidates will also learn the fundamentals of product development, pricing, reinsurance, valuation, financial reporting and administration. This module …
[mathjax] Basic Probability Functions and Moments Probability Density Function \(f(x)=\dfrac{d}{dx}F(x)\) or \(f(x)=-\dfrac{d}{dx}S(x)\) Hazard Rate Function \(\mu (x)=h(x)=\dfrac{f(x)}{S(x)}=-\dfrac{d\ln S(x)}{dx}\) Cumulative Hazard Rate Function \(H(x)=\int_{-\infty }^{x}{h(t)dt}=-\ln S(x)\) \(S(x)=e^{-H(x)}=e^{-\int_{-\infty }^{x}{h(t)dt}}\) Moment of X nth Raw Moment of X: \(\mu’_{n}=E[x^n]\) nth Central Moment of X: \(\mu_n=E[{(x-\mu )}^n]\) Covariance: \(Cov(X,Y)=E[(X-\mu_X)(Y-\mu_Y)]=E[XY]-E[X]E[Y]\) Correlation Coefficient: \(\rho_{XY}=Cov(X,Y)/({\sigma_X}{\sigma_Y})\) Coefficient of Variance: \(\sigma /\mu \) Skewness: \(\gamma_1=\mu_3/\sigma^3\) Kurtosis: \(\gamma_2=\mu_4/\sigma^4\) Moment Generating …
Basic Calculus Integrations \(\dfrac{d}{dx}a^x=a^x\ln(a)\) \(\int{{{}\over{}}a^xdx}=\dfrac{a^x}{\ln(a)}\text{ for }a>0\) Logarithmic Differentiation \(\dfrac{df(x)}{dx}=f(x)(\dfrac{d\ln f(x)}{dx})\), since \(\dfrac{d\ln f(x)}{dx}=\dfrac{df(x)/dx}{f(x)}\) Partial Fraction Decomposition \(\int{{{x}\over{1+x}}dx}=\int{(1-{{1}\over{1+x}})dx}\) Integration by Parts \(\int{udv}=uv-\int{vdu}\) Special Cases: \(\int_{0}^{\infty }{xe^{-ax}dx}=\dfrac{1}{a^2}\), for \(a>0\) \(\int_{0}^{\infty }{x^2e^{-ax}dx}=\dfrac{2}{a^3}\), for \(a>0\) Sets Set Properties Associative Property \((A\cup B)\cup C=A\cup (B\cup C)\) and \((A\cap B)\cap C=A\cap (B\cap C)\) Distributive Property \(A\cup (B\cap C)=(A\cup B)\cap (A\cup C))\) …
[mathjax] Review Basic Concepts – Integrals: \(\int_{0}^{\infty }{{{t}^{n}}{{e}^{-ct}}dt}=\dfrac{n!}{{{c}^{n+1}}}\) \(\int_{0}^{u}{{{t}^{n}}{{e}^{-ct}}dt}=\dfrac{1-(1+cu){{e}^{-cu}}}{{{c}^{2}}}\) \({{(\bar{I}\bar{a})}_{u}}=\dfrac{{{{\bar{a}}}_{\overline{u}}}-u{{v}^{u}}}{\delta }\) – Geometric Series: \(\sum\nolimits_{k=0}^{n-1}{a{{r}^{k}}}=a\dfrac{1-{{r}^{n}}}{1-r}\) \({{i}^{(m)}}=m({{(1+i)}^{{}^{1}/{}_{m}}}-1)\) \({{d}^{(m)}}=m(1-{{(1+i)}^{-{}^{1}/{}_{m}}})\) – Survival Function: \({{S}_{x}}(0)=1\) \(\underset{t\to \infty }{\mathop{\lim }}\,{{S}_{x}}(t)=0\) \({{S}_{x}}(t)\) must be a non-increasing function of t Review from MFE – Rate of Discount: \(d=\dfrac{i}{1+i}\) – Discounting Rate: \(v=\dfrac{1}{1+i}=1-d\) – Continuously Compounded Interest Rate: \(\delta =\ln (1+i)\) – Simple Interest Rate i: \({i}_{t}=1+it\) , \({{v}_{t}}=\dfrac{1}{1+it}\) – PV of …
Accounting Principles
Product Classification Why need product classification? Not all products manufactured by insurance companies are insurance contracts Insurance contracts are those that contain significant insurance risk How products are classified? For valuation purposes, insurance contracts can be further classified into: Ordinary Life – Participating Ordinary Life – Non-Participating Personal Accident Unit-linked (Contracts with an explicit account balance) Universal life (Contracts with …
Introduction IFRS 17 Insurance Contracts establishes principles for the recognition, measurement, presentation and disclosure of insurance contracts issued. It also requires similar principles to be applied to reinsurance contracts held and investment contracts with discretionary participation features issued. The objective is to ensure that entities provide relevant information in a way that faithfully represents those contracts. This information gives a …
Coding & Programming
Purpose Extended formulas enhance and extend the capabilities of the Prophet programming language. They enable more complex calculations to be carried out than standard Prophet formulas. They are also able to retain the values that they have calculated from one model point to the next and from one loop to the next in a dynamic or stochastic run. Examples of …
Q_A_EXP IF ZERO_MORT = 1 AND AGE_AT_ENTRY < ZERO_TOL_AGE THEN 0 ELSE IF WL_POLICY = 1 AND t
Definition Types Definition type Description Formula A formula expressed in Prophet’s programming language. Constant A constant value. Global The value is read from the global file at run time. Parameter The value is read from a parameter file at run time. Model point The value for each model point is read from the model point file at run time. Generic …