Kindly solve this economics question precisely. Thank you

Felicity is a fund manager who is considering investing Elm in a specialist investment contract where the return depends on the performance of a particular company. She has a choice between two contracts as follows: . Long contract: if the company is deemed a "success", the investment will return +100% and if it is deemed a "failure" it will return -75% Short contract: if the company is deemed a "success", the investment will return -50% and if it is deemed a "failure" it will return +50%. Before she decides which contract to invest in, Felicity will be able to observe the investment performance of the company's shares relative to the stock market. Companies that are "successes" have a 60% probability of outperforming the stock market. Companies that are "failures" have a 40% probability of outperforming the market. List Felicity's four decision functions [2] (ii) Calculate the values of the risk function for each decision function and type of company. 16] Two thirds of such companies under consideration are known to be failures. (iii) Determine Felicity's optimal decision function. [3] [Total 11] Claims on a portfolio of insurance policies arrive as a Poisson process with parameter A, claim amounts having a Normal distribution with mean p and variance oh, and there is a loading 0 on premiums. The insurance company has an initial surplus of U. Explain carefully the meaning of Y(U). P[V.) and (U.1). 13] (ii) State four factors that affect the size of (U(), for a given r [2] (iii) Explain, for each factor, what happens to 'P(U.() when the factor increases. [4] Sarah, the insurance company's actuary, prefers to consider the probability of ruin in discrete rather than continuous time. (iv) Explain an advantage and disadvantage of Sarah's approach. [2] [Total 11]