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4

Well, according to what I see, let us take each part of the value function by its own and then $$\underbrace{\pi((t_1,t_1)|G)}_{1/2}\underbrace{\sigma((a_1,a_2)|(t_1,t_1),G)}_{3/5\times 3/5=9/25}\underbrace{u_1((a_1,a_2),G)}_{8}=36/25$$ $$\underbrace{\pi((t_1,t_2)|G)}_{1/2}\underbrace{\sigma((a_1,p_2)|(t_1,t_2),G)}_{3/5\times 2/5=6/25}\underbrace{u_1((a_1,...


3

The trade-off between risk and expected returns depends on your own preferences. Assume that you are expected utility maximizer and let the return of the investment be given by the random variable $X$. Your utility is given by. $$ \mathbb{E}(u(X)) $$ Let $\mu$ be the mean of $X$ and let $\sigma^2$ be the variance of $X$ then taking a Taylor expansion of $u(x)...


0

First, $l(\tau)(y)$ is a function of both $\tau$ and $y$, and the dependence on $\tau$ is essential; this is how communication happens. Since $T$ and $Y$ are finite, there is no point in introducing integrals. $\mathbb{E}_{l(\tau)}g(F(y))$ is the expectation over the function when the random value $y$ is distributed according to $l(\tau)$. That is, $$\mathbb{...


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