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Unformatted text preview: MAFS 5030 Quantitative Modeling of Derivatives Securities Homework Two Course Instructor: Prof. Y.K. Kwok 1. Show that a dominant trading strategy exists if and only if there exists a trading strategy satisfying V < and V 1 ( ω ) ≥ 0 for all ω ∈ Ω. Hint: Consider the dominant trading strategy H = ( h h 1 ··· h M ) T satisfying V = 0 and V 1 ( ω ) > 0 for all ω ∈ Ω. Take G * min = min ω G * ( ω ) > 0 and define a new trading strategy with hatwide h m = h m , m = 1 , ··· , M and hatwide h =- G * min- M summationdisplay m =1 h m S * m (0). 2. Consider a portfolio with one risky security and the riskfree security. Suppose the price of the risky asset at time 0 is 4 and the possible values of the t = 1 price are 1 . 1 , 2 . 2 and 3 . 3 (3 possible states of the world at the end of a single trading period). Let the riskfree interest rate r be 0 . 1 and take the price of the riskfree security at t = 0 to be unity. (a) Show that the trading strategy: h = 4 and h 1 =- 1 is a dominant trading strategy that starts with zero wealth and ends with positive wealth with certainty....
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- Spring '11