Fourth Year Research Projects

Mathematics

1) Mandelbrot set

                        Students : K.B.V.S.Thakshila, S.H.Rathnayake, S.H.Y.Kottegoda
                        Supervised by Mr.C.J.Wijeratne

The main topic discussed in this report, namely, the Mandelbrot set is one of the most elegant pictures that have captured the attention of Mathematicians in the recent years.

Generated by a simple quadratic equation of complex numbers, the Mandelbrot set produces pictures with an incredible amount of structure in it. This is exactly the interesting fact about this set. Indeed the Mandelbrot set is rich in self similarity though it is apparently a very complex picture.

Moreover there is a beautiful relationship between the Mandelbrot set and two other dynamical systems, namely, the Julia set and the orbit diagram. We have tried our best here, to view the Mandelbrot set in finer views using various methods of drawing pictures of the set.

 

Finance & Business Mathematics

1) Investing In Stock Exchange and Optimizing the Portfolio Using Quadratic Programming.

                        Students : Lochana Siriwardena, Namal Adhihetty
                        Supervised by Mr.M.H.K.M.Hameem

Stocks will provide investors with above-average long term investment return opportunities. But it is a risk-return tradeoff. In order to obtain greater returns on investments, the investor must be willing to take on greater risk. Investors prefer higher returns for lower risks. Our task here is explaining the functions of stock exchanges and techniques used in calculating the return of the portfolio. A method to maintain an efficient portfolio is suggested by minimizing the risk associated with the portfolio. To fulfill this Quadratic programming is used. Since we assume the present performance of a stock is reflected by the past performance s ome past data (returns) of the stocks in the portfolio is been analyzed. The following well-respected strategies given in this dissertation are among the most commonly used for investing in stocks.

 

2) Development of a pricing & profitability evaluation model for Term Assurance plans

                        Students : D. M. Peiris, H.A.A. Priyadarshani
                        Supervised by Dr. R.T. Samaratunge, Mr. Pushpakumar Gunasekara and Mr. Hugh Terry

Term assurance is the cheapest and simplest form of life cover, providing life assurance for a fixed term only where the assured is payable only if the life assured dies within that term. In order for a company to issue such a policy it should price the product accordingly for the Sri Lankan insurance market which would in return bring them profit. Having this as our main aim of the project we developed a model to price a product and evaluate its profitability.

Thus, in developing the model the first stage was constructing the mortality table using the mortality rates of the A67/70 Mortality table. A basis was established and the pricing of the product was done on it. The gross premium (price of the product) was calculated and a rate table was constructed on it. Observing the values of the rate table, variations were minimized and premiums were changed for profitability purposes. In addition, the reserve to be maintained was calculated in terms of net level premiums, since the company has an obligation towards the policyholder right through out the term.

Further the profitability was evaluated first constructing a revenue account. Through different measures the profitability of the product is appraised. Also a sensitivity analysis was done on some main variables affecting the profit .Further a comparison with actual pricing in the Sri Lankan market was done to evaluate the prices obtained from the model. The report finally aims in concluding the more profitable policies to be issued. For longer terms (Terms 15 to 20) and for ages between 35 and 60 are generally more profitable. For early ages a profit margin should be added to prices obtained or prices of the smoothened rate table should be taken. The sensitiveness of Mortality rates, Lapse rates is higher on profitability. Rates are lower than actual pricing for few reasons such as model does not include payments such as surrender payments etc.