# CT-4 Models: An Introductory Brief

Model building is an art rather than science.

In art, you need to bring out the creativity because you need to mix up things in such a manner that it ultimately looks good.

CT-4: Models, primarily focuses to strengthen the concept of Actuarial Modelling among the actuarial aspirants. It is an insightful and interesting paper yet challenging. Being a statistics-based paper, it provides grounding in stochastic processes as well as survival models and their applications.

Plus the models explained here are further included along with there advance versions in higher actuarial exams. More than that, the Markov Process derived models discussed in CT-4 are widely used in the general insurance sector.

So, without further ado, let’s unravel the CT-4 coursework.

The course comprises a total of thirteen chapters which are segregated into four sections.

The course isn’t quite vast but you need to emphasize on understanding each and every concept under Stochastic Process, i.e. the first six chapters. Followed by brushing up your prompt evaluation of various empirical based survival models and to draw inferences from it.

To help you understand the content better, I’ll be explaining to you the objectives of the paper section wise, so let’s begin:

##### SECTION-1 (FOUNDATIONAL)
• Principles of Actuarial modeling are discussed.
• The need and use of the model, how to analyze the output and test the appropriateness of the model.
• Definitions of various terms and types of stochastic processes.
• Markov property in reference to the stochastic processes. To discuss the chief features and examples of Markov Chain model.
• Calculating the stationary and long-run distribution for a Markov Chain.
• Introduction of two-state Markov model.
##### SECTION-2 (CONCEPTUAL)
• Introduction of time-homogeneous and time-inhomogeneous Markov Jump Processes.
• State and prove Chapman-Kolmogorov equations.
• Explaining and analyzing various survival models, sickness models, and marriage models in terms of a Markov Process.
• Defining the Poisson Process.
• Deriving time independent and time/age dependent transition intensities.
##### SECTION-3 (APPLICATIVE)
• To model the lifetime of an individually aged x as a random variable.
• Describe the distribution and density functions of the future lifetime (random), evaluate survival function, death density function and hazard function and to derive the relationship between them.
• Derive expected value and variance of the curtate future lifetime and complete future lifetime random variable.
• Define censoring and it’s types.
• Introduction to Kaplan-Meier Model and Nelson-Aalen Model and estimate survival functions.
• Describe proportional hazard models and their use to estimate the effect of covariates on the hazard.
• Describethe Cox proportional hazard model.
##### SECTION 4 (APPLICATIVE & THEORETICAL)
• Describe the Binomial model of mortality and estimate transition probabilities and its maximum likelihood estimator.
• Describe the Poisson model of mortality and estimate transition forces and its maximum likelihood estimator.
• Explain the concept of rate interval and census approximation.
• Describe the principle of correspondence and develop census formula at a specific age classified as age next, last or nearest birthday.
• Describe the graduation process and its importance.
• Derive graduated rates from crude rates using graduation by parametric formula, graduation by reference to standard table and graduation by graphical method.

So, all this sums up the syllabus of CT-4. Besides, there are a few common doubts of actuarial aspirants related to this paper which I’m listing below:

Q. What is the update to CT-4 under 2019 curriculum?
Ans. Under 2019 curriculum, CT-4 and CT-6 are merging into a single paper, i.e. CS2: Core Statistical 2. This paper will have two parts. One, the theoretical paper of 3 hrs and 15 mins and an additional practical exam of 1 hr 45 mins using R language. The difficulty level of this paper is expected to increase after the change in curriculum.

Q. What is the right time to give CT-4?
Ans. If you have cleared CT-6 already, then to get the exemption from CS2 (under 2019 curriculum) you are obligated to clear CT-4 before 2019. You can also give CT-4 and CT-6 together, but it is really hard to clear both of the statistical-based exams in a single sitting.

So, if you have CT-6 cleared, then I would advise you to sit for CT-4 in 2018 September diet and be exempted from CS2, else you would have to study CT-6 again along with CT-4 under CS2 plus you have to give a practical exam too.

If none of your exams are cleared, then you should sit for CS2 next year and clear this exam in a single go. Also, the knowledge of R language will help you to develop the practical understanding of the coursework too.

Q. Knowledge of which CT papers will be needed in CT-4?
Ans. Prior knowledge of CT-1 and CT-3 is vital while the basic knowledge of CT-5 is a bonus for you.

Q. How much time should I dedicate to complete the syllabus of CT-4?
Ans. The recommended time is 125-150 hrs. Whereas, the actual time could differ from person-to-person.

Q. What are the passing marks of CT-4 in IAI and IFOA?
Ans. IAI never discloses its passing marks while the cutoff for CT-4 in IFOA usually ranges between 55-60.

Q. What are the passing percentage of CT-4 in IAI and IFOA?
Ans. For the past 5 years, the passing percentage of CT-4 from IAI is quite odd, ranging from 2% to 30%. While in IFOA the scenario is a little better, here the passing rate ranges between 40%-56%.

Q. Is there any need to study additional course material to clear the exam?
Ans. The study material along with X series, Question banks and revision notes are completely enough to ace you through the exam.

Q. On what topics should I be focusing more while studying CT-4?
Ans. Devote a significant amount of time to understand the concepts and properties of various Markov processes discussed and the models associated with them. They carry the highest weight in the exam and have an ample variety of questions. Also, focus on enhancing your calculative abilities while working on survival models. Do emphasize proofs of survival functions and the relationship between them. And, never ever leave the theory mentioned in the last two chapters which explain graduation of crude rates and there testing.

Q. Should I take coaching for CT-4?
Ans. It completely depends on you and your abilities. Although, I would advise you to take coaching for the exam because the teachers teach in a systematic manner and through their experience they able to tell you the important questions and topics for the exam.

Q. Which exams further require the knowledge of CT-4?
Ans. Exams which require knowledge of CT-4 are:

• CT-5: To develop contingencies (death/survival transitions) based on Markov property.
• CT-8: Concepts are further elaborated as discussed in CT-4.
• CA-1 and few ST series exams: Use the principles and models discussed in this exam.

Q. Any tips for CT-4?
Ans. For this paper specifically, surrender yourself to the study material. I have seen many a time that students who are fully prepared and have done ten-years are unable to clear the exam because they aren’t thorough with the concepts and haven’t gone through the study material even once. For statistics-based papers, remember the golden rule: Emphasize more on the concept than doing questions. You can have an infinite variety of questions, but if you know the concept well, no matter how much twisted the question comes, you would be able to solve it correctly.