Summary
Life Insurance Mathematics - Samenvatting Soln Man Actu Maths Life Contingen Risks, ISBN: 9781107620261 Life insurance mathematics
- Course
- Institution
- Book
2nd Year Econometrics Summary
[Show more]
Connected book
Book Title:
Author(s):
- Edition:
- ISBN:
- Edition:
Seller
Follow
feanne1
Reviews received
Content preview
Samenvatting Life Insurance MathematicsLecture 1
Tx = future lifetime of (x)
x + Tx = age at death random variable for (x)
Fx = P[Tx < t] = cumulative dist. Function of Tx
Sx = survival function = 1 - Fx
Assumptions Fx
- Fx must be a non decreasing function
- lim(t-> inf) Fx (t) = 1
- lim(t-> - inf) Fx (t) = 0
Assumptions survival function
- Sx (0) = 1
- Survival function must be a non-increasing function of t
- Sx (t) is di erentiable, t>0
- lim (t->inf) Sx (t) = 0
- lim(t->inf) t Sx (t) = 0
- lim(t->inf) t^2 Sx (t) = 0
μx = force of mortality = Hazard rate
For small dx: μx dx = probability that (x) dies before attaining age x + dx
Lecture 2
E[Tx] = ėx E[Kx] = ex
Var (Tx ) = E[Tx ^2] - (ėx)^2
Curtate future lifetime = Kx = Expected # of whole years lived by (x)
ėx is almost always a decreasing function of x
t = representation of # of survivors to age x+t
E[ _t] = x+t
d_x = represents # of deaths at age x
Multiplication rule
As the outstanding loan ↓ => Term insurance sum insured ↓
Lecture 3
Period life tables ( drawback: generations are mixed )
Cohort life tables ( preferred, but drawback: di cult to predict )
Infant mortality, accident hump and aging process
Fractional age assumptions : about the prob. dist. of the future lifetime r.v. between integer ages
Force of mortality is constant between integer values
Underwriting : sign and accept the liability under an insurance policy
==> guaranteeing payment in case loss or damage occurs
= is a way of reducing the impact of adverse selection for life insurance
𝓁𝓁
𝓁 ff ffi
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller feanne1. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $9.22. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
77254 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now