I want to solve $P(e^{X_1}+Ke^{X_2}
Probability equation
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probability
stochastic-processes
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0Where did the function come from? – 2012-07-13
1 Answers
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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.