# Problem Essay Examples

## Problem Solving

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Problem Solving 1.a). Coordinates of points of inflection f(x)=e-x22f'(x)=(-x)(e-x22)Second derivative = e-x22+e-x22.x2it follows that when 0=e-x22(x2-1)x=±1f(1)=1√eThe points of inflections are (1, 1/√e) and (-1, 1/√e) b).f(x)=x+2sinxfirst derivative =1+2cos x Second derivative =2sinxGetting the local maxima and minima we equate the first derivative to zero 1+2cos x=0cos x=-12x=2π3, 4π3 evaluating the second derivative at x=2π3 and x=4π3-2sin2π3 =-2sin32=-√3. Therefore x=2π3 is a maximum value -2sin4π3 =-2sin-32=√3And x=4π3 minimum C. f(x)=x13(x+4)The first derivative =x13ddx(x+4)+x+4ddxx13=x13+(x+4)(13x23)=x13+(x3x23+43x23)f'(x)=43x23+4x133Using the...

• Words: 825
• Pages: 3

## quantitative finance

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Problem-solving Problem (a) The expected value of the unhedged firm is: 0.5*200/(1+0.05)+0.5*(500-(500-300)*0.4)/(1+0.05)=95.24+200=295.24 Problem (b) Let’s buy put options for gold pricing at 500 with premium P. The expected value of the hedged firm is: (500-(500-300)*0.4)/(1+0.05)-P=420-P Problem (c) The safe debt is the one that pays off not more than 200 in a year. The value of the firm is:0.5*(200-200)/(1+0.05)+0.5*(500-200-(500-200-300)*0.4)/(1+0.05)=142.86 Problem (d) The safe debt is the one that pays off not more than 200 in a year. Let’s buy put options for gold pricing at 500 with premium P. The value of the firm is: (500-200-(500-200-300)*0.4)/(1+0.05)-P=285.71-P Problem...

• Words: 275
• Pages: 1

## 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)....

• Words: 275
• Pages: 1

## Problem 2

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Problem 2Suppose we are analyzing an equilibrium in which the MMs’ strategy is to not acquire information (pn = 0 for n = 1, 2). Argue that in this case, bn = 1/2 in equilibrium. Lack of value information implies that both players are bound to make a bid that is defined by the expectation of the market. In essence, the prospect of attaining bn-V would remain equally distributed among the two market markers. Arguably, the attribute of the trader stands dismissed along the implication of noise. Considering the input of the two market markers, n1 and n2, their ability to achieve bn when the value is unknown would be split evenly MMn1 = bn – V MMn2 = bn – V But V = 0 (since v is...

• Words: 1100
• Pages: 4

## problems

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Problem 15-1B looks into Agler company's manufacturing accounts which manufacture helmets. Various costs items have been classified as either product costs, direct labor, direct materials or manufacturing overheads. Total production costs have been calculated to determine the cost of producing one helmet. Problem 15-2B analysis the manufacturing accounts of Elliot's company which manufactures tennis rackets. After computing the total production costs amounting to \$147,700 incurred to produce 2500 tennis rackets, the cost of producing one racket is \$59.08. Problem 15-3B looks into two cases in which the cost of goods manufactured schedule; income statement and a partial balance sheet are prepared....

• Words: 1375
• Pages: 5

## problems

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problems Abstract This paper looks into the entries made into the books of accounts relating to manufacturing accounts. Various classifications of costs in the manufacturing sector have been used to record each cost item. P15-3A comprises of two cases in which manufacturing costs and selling expenses are listed. The paper seeks to show how the cost of goods manufactured is arrived at, the accompanying income statement and a list of selected current assets. Problem 14-5A looks into the computation of costs of goods manufactured presented in a schedule as well as the income statement for the financial year. Problem 15-4A also looks into the manufacture cost schedule and list of current assets for...

• Words: 825
• Pages: 3