The first step of the strategy design is to establish some starting value for the spending policy. To do so, let us assume a constant rate of growth in spending 2.0% (G = 1.02) per year in real terms, to match the real growth rate in the economy. This implies that both contributions paid into the fund and benefits paid out of the fund grow at the same rate. Let us also assume (contrary to the data) that the fund can invest in a risk-free asset with a constant real return of 3.0% (R = 1.03) per year. Further, let us assume that the pension fund is designed for perpetuity. The initial value of the fund (i.e. the financial wealth of the fund) is V0 = 10 billion USD.

(a) Compute the required initial spending rate s0 of the fund and describe the spending policy in this case. You should also plot the spending S (not the spending rate) over time for the next 50 years (year 0 to year 50), as well as explain how the spending rate will evolve over time.

(b) Under the above scheme, compute the present value of liabilities as well as the probability that the fund may go bankrupt in the future. Explain your answers.