A Erin is an entity consisting of its assets and let A; denote the market value of rm's meets. Asimme that the total asset value follows a stochastic prolo- modeled by =pd+odzh Al- Wl'IEI'E p and 0'2 [almnried to be constant} are the instantaneous mean and varianceJ respectively? of the rate of return on At. Let C and D denote the marlret value of the current liabilities and market value of debt, respectively. Let T be the maturity date of the debt with face value D1". Suppose the current liabilities of amount GT are also payable at time T.f and it constitutes a claim senior to the debt. Jse.f let F denote the present value of total amount of interest and dividends paid ever the term T. For simplicity? F is alarmed to be prepaid at time t = I]. The debt is in default if AT is less than the total amount payable at maturity date T, that is, AT. {2 Dr + G?\" {a} Shew that the probability of default is given by p=~ laws? exam:1 . are\"? (1')} Explain why the expected loan loss L- on the debt is given by \"T +01- '1' EL = [131' + C;- we} [e + [a D;-f[o]l do, D CT where f is the density function of AT. Give the financial interpretation to each integral