Kindly solve all of the following

1.

Craig and Shivon are playing a two person zero sum game. Craig picks an integer / from 1 to n, Shivon picks an integer / from 1 to n, and Shivon receives from Craig: 1 if i- j =1, 0 otherwise. (i) Set out the payoff matrix, 4, in the case that n = 7. [2] Show that A can be reduced to a 4 x 4 matrix by eliminating dominated strategies. [4] Craig and Shivon adopt randomised strategies. (iii) Determine the randomised strategy Shivon should adopt, and the value of the game to her. [2](i) Set out the likely changes to an individual's income and expenditure as a result of retirement. [3] The Net Replacement Ratio (NRR) is often used as a measure of the level of retirement provision. (ii) Explain why an appropriate NRR might vary between individuals. [4] A survey in a developed country has revealed that the average NRR is less than 30%. (iii) Suggest why the NRR is so low. [2] (iv) Discuss ways by which State and employers can help to increase the NRR.[10](i) Describe why the study of behavioural finance is useful in making investment decisions. [2] (ii) Describe the behaviours exhibited in each of the following scenarios: (a) A pension fund actuary is considering what assumptions she should use for inflation and has decided to remain with her assumption from the previous valuation which was produced two years ago. This is despite a currency collapse resulting in the domestic inflation rate increasing substantially. (b) A private investor is considering buying a particular equity and is researching information about that equity. A number of newspapers have written about the equity in question and the investor concentrates his research on those recommending buying the equity. (c) A number of people were asked about the length of a sessional meeting at the Institute and Faculty of Actuaries. Half were asked how long it was and the other half how short it was. Those answering how long it was thought it was over two hours while those answering how short it was thought it was less than two hours. (d) A fund management group is closing one of the funds in its range and has written to the investors in that fund offering them a free transfer to any of their other funds. When looking at the responses, the fund manager finds that most investors have chosen the first fund on the list despite there being a fund lower on the list which is more similar to the fund being closed