lecture2 - Mathematical Problems of E62 Contingent Claims...

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e62: lecture 2 22/09/10 Mathematical Problems of E62 1 Algebraic Geometric linear algebra intersecting hyperplanes linear combinations linear programs polyhedra optima duality constraints versus objective quadratic programs gradients local minima max cx s . t . Ax b x 0 Ax = b min yb s . t . yA c y 0 max cx - 1 2 x T Hx s . t . Ax b x 0 e62: lecture 2 22/09/10 A context and application area for LA and LP A contingent claim is a contract Receive a payoff depending on an uncertain outcome May pay a price to purchase the contract Examples Lottery Insurance Negotiated contract with contingencies Stocks, bonds, options, and other derivatives Mathematical representation Enumerate possible outcomes 1, 2 , . .., M Specify outcome-contingent payoffs Contingent Claims 2 a ∈± M e62: lecture 2 22/09/10 Stocks and Bonds Assume one year holding period 3 stock zero-coupon bond price p 1 p 2 outcomes future stock price = 1 , . .., M future stock price = 1
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lecture2 - Mathematical Problems of E62 Contingent Claims...

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