0.9 0.1 0.0 For the transition matrix P = 0.5 0.1 0.4 0.0 0.7 0.3 matrix P solve the equation SP = S to find the stationary matrix S and the limiting
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- For what values of a does the matrix A=[01a1] have the characteristics below? a A has eigenvalue of multiplicity 2. b A has 1 and 2 as eigenvalues. c A has real eigenvalues.Recall that the general form of a logistic equation for a population is given by P(t)=c1+aebt , such that the initial population at time t=0 is P(0)=P0. Show algebraically that cP(t)P(t)=cP0P0ebt .Find the equilibrium solution for P. Furthermore determine whether P is initially increasing faster if the initial population is 120 or 200.
- B) Let dP/dt =.5P - 50. Find the equilibrium solution for P. Furthermore, determine whether P is intially increasing faster if the initial population is 120 or 200.Consider the geometric Brownian motion with σ = 1: dS = μSdt + SdX, and consider the function F(S) = A + BSα. Find any necessary conditions on A, B, and α such that the function F(S) follows a stochastic process with no drift.9.2 4 solve the equation SP = S to find the stationary matrix S and the limiting matrix P
- You are considering an investment in Justus Corporation's stock, which is expected to pay a dividend of $1.75 a share at the end of the year (D1 = $1.75) and has a beta of 0.9. The risk-free rate is 5.4%, and the market risk premium is 6%. Justus currently sells for $21.00 a share, and its dividend is expected to grow at some constant rate, g. Assuming the market is in equilibrium, what does the market believe will be the stock price at the end of 3 years? (That is, what is ?) Do not round intermediate calculations. Round your answer to the nearest cent.Find values of C1 and C2 so that the given functions will satisfy the prescribed initial conditions.b)Find the matrix exponential ?KL (using the Jordan form) and the analytical solution of ?(?) for arbitrary initial condition ?N.
- The price of a stock is modeled with a geometric Brownian motion with drift μ=-0.25 and volatility σ=0.4. The stock currently sells for $35. Assume that an option is available to purchase the stock in six months for $40. Find the expected payoff of the option.What is your predicted average population growth rate from this method, in terms of lambda AND % per year? Does that predict an increasing or decreasing population, on average? Year (t) Nests at time t Nests at t + 1 N(t+1)/N(t) 1983 746 780 1.046 1984 780 702 0.900 1985 702 744 1.060 1986 744 729 0.980 1987 729 843 1.156 1988 843 905 1.074 1989 905 992 1.096 1990 992 1180 1.190 1991 1180 1275 1.081 1992 1275 1241 0.973 1993 1241 1566 1.262 1994 1566 1930 1.232 1995 1930 1915 0.992 1996 1915 2219 1.159 1997 2219 3482 1.569 1998 3482 3365 0.966 1999 3365 5834 1.734 2000 5834 4927 0.845 2001 4927 5525 1.121 2002 5525 7601 1.376 2003 7601 6446 0.848 2004 6446 9258 1.436 2005 9258 10899 1.177 2006 10899 average 1.1427 Consider the model : Yt =ρYt−1 +β0 +ut State all assumptions. (a) Derive the OLS estimator for ρ and β0. (b) Derive E[ρ]. Is OLS biased ? (c) Derive E[b0]. Is OLS biased ?