## Solution Library

#### Fixed Filtration With Respect To Martingales

QuestionFor a sequence (An) of events, show that  SummaryThe question belongs to Mathematics and it is about fixed filtration with respect to martingales defined.Note: The solution is in handwritten format.Total Word Count NA ... Read More

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#### Calculation Of Martingale

QuestionLet (Xn) be a martingale and write âˆ†n = Xn − Xn−1, Suppose that bm ↑ ∞ and Σ∞m=1 b −2m Eâˆ†2m < ∞. Prove that Xn/bn → 0 a.s.SummaryThe question belongs to Mathematics and it is about martingale calculationNote: The solution is ... Read More

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#### Calculation Of Non-Negative Martingale

Question Let (Xn) be a martingale with supnE|Xn| < ∞. Show that there  is a representation Xn  = Yn – Zn where (Yn) and (Zn) are non-negative martingales such that supn EYn < ∞ and supn EZn < ∞ SummaryThe question belongs to Mathematics and it is about no ... Read More

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#### Martingale Calculation

QuestionLet (Xn) be adapted to (Fn) with 0 ≤ Xn ≤ 1. Let α, β > 0 with α + β = 1. Suppose X0 = x0 and P(Xn+1 = α + βXn|Fn) = Xn, P(Xn+1 = βXn|Fn) = 1 − XnShow that Xn → X∞ a.s., where P(X∞ = 1) = x0 and P(X∞ = 0) = 1− ... Read More

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#### Calculate The Value of Martingale

QuestionSuppose Fn ↑ F∞ and Yn → Y∞ in L1. Show that E(Yn|Fn) →E(Y∞|F∞) in L1SummaryThe question belongs to Mathematics and it deals with calculation of martingaleNote: The solution is in handwritten format.Total Word Count NA ... Read More

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#### Calculate The Total Asset Value Of A Company

QuestionLet Sn be the total assets of an insurance company at the end of year n. Suppose that in year n the company receives premiums of c and pays claims totaling ξn, where ξn are independent with Normal (µ, σ2) distribution, where 0 < µ < c. The company is ruined if i ... Read More

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#### Minimization Calculation Using Simplex Method

QuestionSolve the given minimization problem by the simplex method.Minimize C = –4x – 3ySubject to 2x + 3y ≤ 12         5x – 3y ≤ 9         x ≥ 0, y ≥ 0a. x = 0, y = 4, C = –12b. x = 3, y = 4, C ... Read More

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#### Linear Programming Calculation Using Simplex Method

QuestionSolve the linear programming problem by the simplex methodMinimize C = 9x + 13ySubject to x + 3y ≥ 12         2x + 2y ≥ 8         x ≥ 0, y ≥ 0a. x = –2, y = –2, C = 44b. x = 2, y = 2, C = 44c. x = & ... Read More

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#### Calculation Of Minimization Using Simplex Method

QuestionSolve the given minimization problem by the simplex methodMinimize C = 6x – 2ySubject to 3x + 4y ≤ 24         7x – 4y ≤ 16         x ≥ 0, y ≥ 0a. x = 4, y = 3, C = 18b. x = 16, y = 24, C = 18c. x = ... Read More

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#### Calculation Of Dual Problem Using Simplex Method

QuestionYou are given the final simplex tableau for the dual problem. Give the solution to the primal problem and the associated dual problem.Minimize C = 5x + 4ySubject to 9x + y ≥ 12         4x – 4y ≥ 16         x + ... Read More

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#### Rewriting Linear Programming Problem As Maximization Problem

QuestionRewrite the given linear programming problem as a maximization problem with constraints involving inequalities of the form ≤ (with the exception of the inequalities x ≥ 0, y ≥ 0)Minimize C = 2x + 3ySubject to x + y ≤ 9         x + 2y ≥ 10&nbs ... Read More