Joint Life vs Last Survivor Explained Clearly | Txy = min, Txȳ = max | CM1 Actuarial Mathematics скачать в хорошем качестве

Joint Life vs Last Survivor Explained Clearly | Txy = min, Txȳ = max | CM1 Actuarial Mathematics

Joint Life vs Last Survivor Explained Clearly | Txy = min, Txȳ = max | CM1 Actuarial Mathematics Linkedin   / pratap-padhi   Website https://smearseducation.com/ Join my FREE Skool Community to get all updates and support https://www.skool.com/sme-education-9... Watch my previous recordinds on CS2 Time Series 👉    • Master Time Series Forecasting:Guide to AR...   CS2 Risk Modelling and Survival Analysis 👉   • Why One Random Variable Is Not Enough for ...   👉    • What is a Stochastic Process? Easy explana...   CS1 Previous recorded videos watch 👉    • What are discrete random variables? |Class...   CM1 Previous recorded videos watch 👉    • How to calculate simple interest | Fundame...   👉    • CM1 Y Part2 Class1- A beginner's introduct...   DETAILED TIMESTAMPS 00:00 Why Joint Life Matters in Insurance 01:10 Real-world intuition of two working lives 02:00 Joint Life Status vs Last Survivor Status 03:40 Extending qx and px from one life to two lives 05:00 Meaning of Qxy and why it represents first death 06:30 Why Qxy ≠ Qx × Qy 07:30 Independence assumption explained clearly 09:00 Recap of Tx and complete lifetime 10:40 Density and distribution function refresher 12:00 Link between pxt, qxt and μx+t 14:00 Defining Txy = min(Tx, Ty) 18:00 Logical interpretation of minimum lifetime 22:00 Defining Txȳ = max(Tx, Ty) 24:30 Logical interpretation of maximum lifetime 26:00 Key formulas for Pxy(t) 27:30 Key formulas for Qxy(t) 28:30 Key formulas for Pxȳ(t) and Qxȳ(t) 30:00 Curtate lifetime Kxy 31:30 Curtate lifetime Kxȳ 33:00 Assurance Axy explained 34:30 Immediate payment Āxy explained 36:00 Last survivor assurance Axȳ 37:00 Joint-life annuity intuition 38:30 Last survivor annuity intuition 39:30 Summary and what to expect in next class DESCRIPTION This lecture builds a complete conceptual and mathematical foundation of Joint Life and Last Survivor models in actuarial mathematics. We begin with a simple question: When two lives are involved, what exactly fails first? The first death or the second death? From that single question, we develop the entire structure of joint-life modelling used in CM1. You will clearly understand: • What Joint Life Status means in practical insurance terms • What Last Survivor Status means • Why Txy = min(Tx, Ty) • Why Txȳ = max(Tx, Ty) • Why Pxy(t) = Px(t) × Py(t) under independence • Why Qxy(t) is not equal to Qx(t) × Qy(t) • The role of independence assumption and why it matters • How complete lifetime and curtate lifetime extend to two lives • How Kxy and Kxȳ are defined • How Axy and Axȳ are constructed • How annuities differ under joint life and last survivor • Tx and Kx • Density function and distribution function • Survival probability px and mortality qx • EPV structure for assurances You will see how every two-life formula is a structured extension of single-life logic. This class is conceptual, structured, and exam-oriented. In the next session, we move directly into problem-solving so that you can apply: • k|qxy formulas • Assurance EPV calculations • Joint-life annuities • Last-survivor annuities If you are preparing for CM1 or any actuarial life contingencies exam, this lecture builds the base you must master before attempting joint-life exam questions. #CM1 #ActuarialScience #LifeContingencies #JointLife #LastSurvivor #ActuarialMathematics #InsuranceMathematics #EPV #IFoA #ActuarialExams #SurvivalModels #Mortality #Annuities #Assurance