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Actuarial finance
Consider an investor, who is an expected utility maximizer, with a utility function u (x) = √x. The investor has 100 currency units and the opportunity to take long positions in a bond with the possibility of default (defaultable bond), a swap of Credit default on this bond (credit default swap, CDS), and on a risk-free government bond. A potential default bond costs 96 currency units today and pays 100 six months from now if the issuer does not default and 0 if the issuer defaults. The CDS costs 2 units and pays 100 in six months from today, if the issuer of the bond defaults and nothing more. The risk-free bond costs 99 units today and pays out 100 in six months. The investor believes that the probability of default is 0.02. How many of the 100 monetary units that the investor has to invest in the bond with the possibility of default, in the risk-free bond and in the CDS, respectively?
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