A pension fund needs to select investments for the next two periods, one at a time....

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A pension fund needs to select investments for the next two periods, one at a time. It has in the beginning K million Icelandic kronur (MISK) available for the investments. The fund manager needs your help to select between three available options over the two periods in order to maximize the expected profit at the end. After each period the income will vary depending on the market conditions, which can either be good, neutral or bad. The interest rate for the different investment options is denoted with a where the indexi is used for the three options i € [1,2,3] and the index j is used for the three market conditions j € [1,2,3]. For an example if you invest in option 1 in the beginning of the first period for 10 MISK and the market conditions turn out to be good, then you will get (1+ -1,-1)*10 MISK at the end of period one and be able to use that amount for investing at the beginning of period 2. The probability of the different market conditions for each of the two periods is given with p. a) Draw a scenario tree illustrating the structure of the multi-stage stochastic problem. b) Formulate a multi-stage stochastic programming model which could be used to maximize the expected profit of the investments at the end of the second period. Add the variables to further explain the scenario tree from part a). A pension fund needs to select investments for the next two periods, one at a time. It has in the beginning K million Icelandic kronur (MISK) available for the investments. The fund manager needs your help to select between three available options over the two periods in order to maximize the expected profit at the end. After each period the income will vary depending on the market conditions, which can either be good, neutral or bad. The interest rate for the different investment options is denoted with a where the indexi is used for the three options i € [1,2,3] and the index j is used for the three market conditions j € [1,2,3]. For an example if you invest in option 1 in the beginning of the first period for 10 MISK and the market conditions turn out to be good, then you will get (1+ -1,-1)*10 MISK at the end of period one and be able to use that amount for investing at the beginning of period 2. The probability of the different market conditions for each of the two periods is given with p. a) Draw a scenario tree illustrating the structure of the multi-stage stochastic problem. b) Formulate a multi-stage stochastic programming model which could be used to maximize the expected profit of the investments at the end of the second period. Add the variables to further explain the scenario tree from part a).

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a To draw a scenario tree for this problem you can start by representing the three investment option... View the full answer