1
$\begingroup$

I want to solve $P(e^{X_1}+Ke^{X_2}

  • 0
    Did you want to add that X1 and X2 are independent? Is there some statistical test that led you to the function of X1 and x2 that you have?2012-07-12
  • 0
    @MichaelChernick, yes $X_1,X_2$ are independent2012-07-13
  • 0
    Where did the function come from?2012-07-13

1 Answers 1

1

As long as you can evaluate $P(...) = f(K)$ for any fixed value of $K$, which you suggest doing by Monte-Carlo, you now have a 1-dimensional root-finding problem, e.g. find the value of $K$ such that $f(K)=\alpha$, where $\alpha$ and $f$ are known.

Numerically, such problems are typically solved by Newton's method http://en.wikipedia.org/wiki/Newton's_method for well-behaving $f$ (need existence of and ability to compute $f'(K)$, which you have) or by the Secant or Bisection methods http://en.wikipedia.org/wiki/Bisection_method and http://en.wikipedia.org/wiki/Secant_method.