Hi, 1) September 2021: Q3: Why is c = lambda * (1+theta) * E(X) instead of just (1+theta) * E(X)? Why is the rate of premium income related to the parameter? Is this applicable generally? 2) April 2022: Q4: Why in this long derivation do the ASET solutions include a'(T-t) instead of just -a? If partially differentiating by t - do we not just use -1? I thought T would not be impacted by this differentiation. 3) Under the Merton-Model - THI(d_2) = the probability of assets being greater than the debt i.e. P(S_T > K) Is THI(d_1) of any interest in the Merton model? And what do THI(d_2) and THI(d_1) mean in use cases outside the Merton Model? 4) In the CAPM Pricing Model I am having a bit of struggle understanding the meaning behind each of the formulas. The capital market line: E_p = r + sigma_p/sigma_m * (E_M-r) Market price of risk: (E_M - r)/sigma_M Security Market Line: E_p = r + Beta_P(E_M - r) In the market price of risk - in certain questions I have seen that you exclude the risk free asset from this calculation - as the risk free asset it not involved. However, where do you include the risk free asset elsewhere? Can you use it in the capital market line? What is the intuitive difference between the capital market line and security market line? When would I choose to use either equation? 5) In tutorial 3: Q8)iii) Do we always assume share price follows geometric brownian motian (lognormal model) under the black scholes model? In chapter 8 we find: S_T = S_0 exp((mu - 1/2 sigma^2) T + sigma W_t) in chapter 9 we find: ln S_u - ln S_t ~ N(nu(mu-t), sigma^2(mu-t)) Where do we find that log S_1 ~ N[log S_0 + r - 1/2 sigma^2, sigma^2]? and then - in Q10)i) why do we have the additional (T-t) term in the mean and variance? Why do we believe that the £1.50 term in Q10)i) is not required under the "gift" provision?
