Mathematical Finance

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Problem-Solving Name Institution Problem Solving Part 1 V(t,x) =f(t)log(x+gty)+h(t) = =Vt-12(u-rδ)2VX2VXX+rxVX-βV+yVx+maxc-cVX+u1c=0=Vt-logu-rδVX2VXX +rxVX-βV+yVx+maxc-cVX+u1c=0Focusing on the time limit Such that Rearranginging Deviding by h Taking limits as h0 s.t The economic interpretation of g(t)y is labor income at the time, t. Part 2 2. 1. Optimal Trading Strategy Wealth process dXtπ=πtTμtdt+σtdWt+Xtπ-1nTπtX0=x0y=EβTI(βTST, where I is the optimal trading. where , and is uniquely determined by 2.2. Optimal Consumption in terms of X(t)+g(t)y= Such that,left952500 = Reference Bensoussan, A., & Zhang, Q. (2009). Mathematical modeling and numerical methods in finance. Amsterdam:

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