Consider the risk-sensitive model in XXXXXXXXXXgiven initial state x 1 , θ > 0 , H = 2 , and ε 1 ∼ N(μ,Σ) , the multivariate normal distribution with mean μ and variance- covariance matrix, Σ . Show...

Consider the risk-sensitive model in (10.7) given initial state x₁
, θ > 0 , H = 2 , and ε₁
∼ N(μ,Σ) , the multivariate normal distribution with mean μ and variance-_covariance
matrix, Σ . Show that solving (10.7) is equivalent to solving the min-max problem

i.e., u₁
optimal in (10.8) is also optimal in (10.7) and vice versa as long as both problems have finite optimal values. To do this, first show that

for some constant k (independent of x ) for any positive definite quadratic function Q(x,y) .