# Messages

The results are now available on StudentWeb and a proposed solution for the exam is uploaded in the exam folder.

Have a great summer vacation.

Amine

I have uploaded the solution to the mock exam as well as to problem 3 from the 2014 exam. Note that the solution to this problem is similar to the one in the mock exam, modulo a change in P from 15000 to 20000.

You can try preparing for the exam by solving the 2015 exam remembering that problem 3 with stochastic interest rate is not part of the curriculum.

Next Tuesday I will be available in VBAuditorium 2 if you have any questions.

Finally, I wish you good luck for the exam and remember that you can always reach me by email or in person on the 8th floor.

PS: Some of you asked me for a good book on stochastic analysis and finance and two books that I can highly recommend are:

-Fred Espen Bent's Option Theory with Stochastic Analysis.

-Steven Shreve’s Stochastic Calculus for Finance.

You can now find the Mock exam and the syllabus each in their respective folder.

In the previous lecture we revisited the main results of the course highlighting the most important ones. We also went thorough two of the problems from the 2014 exam.

Next time we meet, we will go through a mock exam in order to prepare for the final one.

I will post, by next week, the active syllabus as well as the mock exam.

You can now find the solution to the 2014 exam in the solutions folder.

Have a great 17th of May!

In the previous lecture we looked at the equation satisfied by the *prospective reserve of a unit-linked pure endowment*, namely *Thiele's partial differential equation*. We also went through *Exercises 8&9* where we looked at the *Black and Scholes pricing formula*.

Next week, we will do a small repetition of the main results of this course and after that we will go through the *Exam from 2014 (Except Problem 4)*.

Please prepare *Problems 3&4* from *Exercises 9*.

You can find the exam from 2014 in the exercises folder.

In the previous lecture, we defined the notion of a *fair price of a contingent claim* and we used this in the framework of *pricing unit linked insurance policies*.

Next time we will take a look at the equation that the prospective reserve of a unit linked insurance policy satisfies, namely *Thiele's partial differential equation*.

Please prepare *Problem 3 from Exercises 8* and *Problems 1&2 from Exercises 9* for next week.

In the previous lecture we started looking at *Chapter 8* on *unit linked insurance policies* where we introduced some fundamental concepts and results from finance. Next week we will introduce the concept of a *fair price of a contingent claim* and see how this can be applied in our setting in order to price unit linked insurance policies.

Work through* Problems 1 and 2 in exercises 8* for next week.

Lecture notes and a solution to exercises 7 are now uploaded on the webpage.

Last time, we went through Exercises 6 where we applied many of the ideas from chapter 6. After that, we looked at chapter 7 concerning Hattendorff's theorem and we proved it in a general setting.

Next week we will start with chapter 8 on unit linked policies and we will introduce many concepts from finance that are fundamental in pricing and hedging financial contracts.

I have uploaded the lecture notes and the solutions to the problems from last time, as well as the problem set for next week.

In problem 3, you only need to report the value of the prospective reserve for state 1 at time* t = 0 *i.e. the one-time premium.

Last lecture we finished the crash course on *stochastic integration with respect to jump processes* by stating *Ito's lemma* and looking at an example of its application.

Next lecture we will look at *Hattendorff's theorem* (i.e. Chapter 7 in the book) and go through *Exercises 6*.

I have uploaded the Exercises for next week as well as the lecture notes on stochastic integration.

After going through the Problems in Exercises 5 we looked at some applications of Thiele's diff. equations, we also started our discussion of stochastic integration with respect to jump processes.

Next week we are going to continue the crash course on stochastic integration with the aim of arriving at the celebrated Ito's lemma in its general form.

I have uploaded the solutions to the problems we went through last time as well as the spreadsheets used in the calculations.

There will be no exercises for next week due to the mandatory assignment which is going to be published on this webpage by tomorrow.

Last time we went through problems in* Exercises 2,3 and 4*. I have posted the solutions to these problems alongside the spreadsheets used in the computations.

Next time we will look at some *further examples of applications of Thiele's difference\differential equations*. We will also go through some of the problems in *Exercises 5*.

God påske!

Last lecture we stated and proved *Thiele's difference/differential equations *and we saw some examples of their use in determining reserves and yearly premiums. In addition, we discussed why *distributional characteristics*, such as higher moments, of the mathematical reserve are important for the insurer and we looked at two difference equations that can be used to calculate these.

I have uploaded the lecture notes for *Chapters 4* and *5* and I have also uploaded *Exercises 3 and 4*.

Next week we will go through *Problems 1 and 3* from *Exercises 2* and the majority of problems in* Exercises 3 and 4.* If time permits, we will look at some of the examples from *Chapter 6* in the book.

Last time we started our discussion of *chapter 4 *on *reserves.* We introduced the concept of *(stochastic) cash flows* and defined the concept of integrating with respect to it and arrived at a definition of *(stochastic) reserves*.

Next time we will continue with *Thm 4.6.3* in the book. This is an important result that enables us to write the reserves in an explicit form (*Thm 4.6.10*).

I have now uploaded *Exercises 2* and you can start working with *Problems 1,2 and 3.*

In addition, you can find a small discussion on the construction of Yield curves in the case of US treasury yields. Note that in practice one does not construct the Yield curve based only on ZCBs but based on different interest rate derivatives (SWAPs, FRAs...).

Last time we finished chapter 3 where we have discussed* interest rates* and how they are modeled in finance and insurance.

Next time we will start our discussion of the main topic of this course namely *Reserves. Chapter 4* starts with the concepts of cash flows, mathematical and prospective reserves and ends by introducing the most important equation for explicit calculations of the reserves i.e Thiele's difference equation.

I have uploaded the solution to all of the problems in Exercises 1 including the numerical part of Problem 4. In addition I have uploaded the lecture notes for the first three chapters and the R-code used last time for fitting the Generalized Gompertz-Makeham model.

The student representaives for STK4500-Spring2016 are:

Eskeland, Karoline (karoline.eskeland (/a) gmail . com)

Tankmo, Joël Fomete (joelfomete (/a) gmail . com)

After finishing our discussion on *Markov chains* by stating and proving the *backward* and *forward Kolmogorov equations* we looked at a quick review of methods used in *mortality modelling and forecasting* (Take a look at the slides and code used during the discussion).

Next time we will start with* chapter 3 on interest rates*.

Please prepare problem 4 in ex1 for next time. I'll present a solution (Finally!) to this problem during the first hour and in addition I'll discuss *the generalized Gompertz Makeham model* in more details.

I have now uploaded the *lecture notes (Manus)* for the first two chapters.

The first lecture is going to be on Tuesday 26th of January.

See you then.