l*******l
发帖数: 248 | 1 1. How do you calculate a standard normal variable (e.g. given x ~ U( 0, 1
), how do you calculate exp( N( x ) )? What probability
distribution is this? What is it's expectation?
2.Suppose you have a mean-reverting stochastic process starting at 0 with
constant drift speed a and volatility coefficient v. What is the variance
of this process? In the limit (e.g. as t -> infinity)? Intuitively, what is
going on here (e.g. describe what's happening and the effect of a and v on
the answer).
var是v^2*t吗？t->inf的时候，var也无穷大吗？a如果足够大的话能很快把var拉回来
吗？ | m*******t
发帖数: 6 | 2 For the first one, do you mean how to use uniform distribution to
generate normal? Then there will be several methods like box-muller,
accept-reject. And for exp(N(x)) this is typical log normal. it's mean
is exp(1/2) for N(x) is standard normal.
the second one, by using the integrator factor, mean reverting process
is explicitly solved(for constant drift speed and volatility). The
stationary variance approaches a constant not infinity. You could read
the details from Shreve's Book.
Just a recommendation(Not mean to you), please carefully read some basic
probability and stochastic books before taking look into those problems.
To understand the basic is more than "Problem Sea" Strategy:) Shreve's
book is really good for fresh quants.
0, 1
with
variance
what is
v on
【在 l*******l 的大作中提到】
: 1. How do you calculate a standard normal variable (e.g. given x ~ U( 0, 1
: ), how do you calculate exp( N( x ) )? What probability
: distribution is this? What is it's expectation?
: 2.Suppose you have a mean-reverting stochastic process starting at 0 with
: constant drift speed a and volatility coefficient v. What is the variance
: of this process? In the limit (e.g. as t -> infinity)? Intuitively, what is
: going on here (e.g. describe what's happening and the effect of a and v on
: the answer).
: var是v^2*t吗？t->inf的时候，var也无穷大吗？a如果足够大的话能很快把var拉回来
: 吗？
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