3. (a) Describe in some detail the two fundamental theorems of finance, and show how the risk-neutral measure is derived in an arbitrage free market which has N risky securities and each having a finite number M of discrete values depending on the M states of the economy. Also describe in some detail how a contingent claim on these securities can be priced. (b) For the special case of the Black-Scholes market, using the concept of a portfolio, discuss how these fundamental theorems facilitate the pricing of any contingent claim. (c) Define an incomplete market where assets are called factors. Consider a contingent claim on the factors of this market. Discuss in some detail, how a liquid market for contingent claims on these factors can be generated and priced to create an arbitrage free market. 3. (a) Describe in some detail the two fundamental theorems of finance, and show how the risk-neutral measure is derived in an arbitrage free market which has N risky securities and each having a finite number M of discrete values depending on the M states of the economy. Also describe in some detail how a contingent claim on these securities can be priced. (b) For the special case of the Black-Scholes market, using the concept of a portfolio, discuss how these fundamental theorems facilitate the pricing of any contingent claim. (c) Define an incomplete market where assets are called factors. Consider a contingent claim on the factors of this market. Discuss in some detail, how a liquid market for contingent claims on these factors can be generated and priced to create an arbitrage free market